{"id":41,"date":"2023-06-05T12:31:43","date_gmt":"2023-06-05T12:31:43","guid":{"rendered":"http:\/\/193.194.89.179\/wp_lrecits\/?page_id=41"},"modified":"2025-01-07T10:01:42","modified_gmt":"2025-01-07T10:01:42","slug":"presentation","status":"publish","type":"page","link":"https:\/\/lrecits.usthb.dz\/index.php\/equipes\/presentation\/","title":{"rendered":"Combinatoire, Arithm\u00e9tique et Informatique Th\u00e9orique (CATI)"},"content":{"rendered":"\n
Equipe<\/td>Combinatoire, Arithm\u00e9tique et Informatique Th\u00e9orique (CATI)\"\"<\/td><\/tr>
Responsable<\/td>Pr. BELBACHIR Hac\u00e8ne<\/td><\/tr>
Mail<\/td>hbelbachir@usthb.dz<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Pr\u00e9sentation<\/strong><\/p>\n\n\n\n

La th\u00e9matique de l\u2019\u00e9quipe se r\u00e9partie sur trois volets.Un volet, relatif \u00e0 la combinatoire, s\u2019articule autour de deux axes. Le premier s\u2019int\u00e9resse \u00e0 la combinatoire \u00e9num\u00e9rative et \u00e0 l\u2019informatique th\u00e9orique. Il porte sur l\u2019\u00e9tude de l\u2019unimodalit\u00e9 de suites r\u00e9currentes lin\u00e9aires, d\u2019hypercubes, de mots, d\u2019automates, de fonctions g\u00e9n\u00e9ratrices, etc\u2026 Une de ses applications est le calcul de la complexit\u00e9 algorithmique. Le second axe s\u2019int\u00e9resse \u00e0 la combinatoire alg\u00e9brique \u00e0 l\u2019aide de structures combinatoires comme l\u2019alg\u00e8bre des fonctions sym\u00e9triques en se focalisant sur les propri\u00e9t\u00e9s et les applications des hyperd\u00e9terminants.Le second volet est relatif \u00e0 l\u2019arithm\u00e9tique et \u00e0 la dynamique des suites et polyn\u00f4mes classiques. Il comprend trois directions. La premi\u00e8re est l\u2019\u00e9tude des suites et des polyn\u00f4mes de Fibonacci, Lucas, Jacobsthal, Stirling, Bell, Bernoulli, Euler, harmonique et des g\u00e9n\u00e9ralisations s\u2019y rapportant. Nous aurons \u00e0 \u00e9tudier particuli\u00e8rement les polyn\u00f4mes d\u2019Appel et les polyn\u00f4mes orthogonaux. La deuxi\u00e8me direction que nous souhaitons investir concerne l\u2019\u00e9tude de la dynamique des suites via l\u2019entropie topologique, les mesures invariantes et les attracteurs. La troisi\u00e8me direction est en relation avec la th\u00e9orie analytique des nombres, plus pr\u00e9cis\u00e9ment elle concerne les d\u00e9veloppements asymptotiques relatifs aux fonctions arithm\u00e9tiques li\u00e9es aux nombres premiers.Le troisi\u00e8me volet se rapporte \u00e0 l\u2019\u00e9conom\u00e9trie. Il concerne deux axes. Un premier aspect concerne l\u2019application de l\u2019\u00e9conom\u00e9trie des variables qualitatives aux donn\u00e9es socio-\u00e9conomiques (comme les donn\u00e9es de la formation professionnelle). Ce dernier aspect a des incidences directes en recherche et d\u00e9veloppement. Le second aspect concerne l\u2019\u00e9tude des plans d\u2019\u00e9chantillonnage en contr\u00f4le statistique de qualit\u00e9.<\/p>\n\n\n\n

Membres<\/h2>\n\n\n\n
BELBACHIR Hac\u00e8ne<\/td>Pr.<\/td><\/tr>
AHMIA Moussa<\/td>MCA<\/td><\/tr>
BELKHIR Amine<\/td>MCB<\/td><\/tr>
BELLAL BOULALOUA Rima narimene<\/td>MCB<\/td><\/tr>
TEBTOUB SEMMANA Assia Fettouma<\/td>MCB<\/td><\/tr>
BOUSBAA Imad Eddine<\/td>MCB<\/td><\/tr>
SOUDDI SOUDDI Nassira<\/td>MCB<\/td><\/tr>
BENMEZAI Athmane<\/td>MCB<\/td><\/tr>
LAMINI el-sedik<\/td>MRB<\/td><\/tr>
ABBAD Sadjia<\/td>MAA, Doc.<\/td><\/tr>
AIT-AMRANE NOUREDDINE Nacima Rosa<\/td>MAA, Doc.<\/td><\/tr>
DJELLAL Toufik<\/td>MAA, Doc.<\/td><\/tr>
OULD MOHAMED CHEBAIKI Ryma<\/td>MAA, Doc.<\/td><\/tr>
ZEGGADA Hamza<\/td>MAA, Doc.<\/td><\/tr>
HADJ BRAHIM Slimane<\/td>MAA<\/td><\/tr>
MEDJERREDINE MANSOUR Assia<\/td>MAA<\/td><\/tr>
HARIK Hakim<\/td>CR<\/td><\/tr>
AMROUCHE Said<\/td>Doc.<\/td><\/tr>
ARABI Abderrahim<\/td>Doc.<\/td><\/tr>
ATTOU Samira<\/td>Doc.<\/td><\/tr>
BELAGGOUN Nassima<\/td>Doc.<\/td><\/tr>
BENAHMED Mohamed<\/td>Doc.<\/td><\/tr>
BENRABIA Im\u00e8ne<\/td>Doc.<\/td><\/tr>
BOUKHECHE Safia<\/td>Doc.<\/td><\/tr>
DJELLAS Ihab eddine<\/td>Doc.<\/td><\/tr>
DJEMMADA Yahia<\/td>Doc.<\/td><\/tr>
IGUEROUFA Oussama<\/td>Doc.<\/td><\/tr>
MEHDAOUI Abdelghani<\/td>Doc.<\/td><\/tr>
MESSEGUEM Oussama<\/td>Doc.<\/td><\/tr>
OTMANI Yassine<\/td>Doc.<\/td><\/tr>
RAMI Fella<\/td>Doc.<\/td><\/tr>
TEBTOUB Soumeya Merwa<\/td>Doc.<\/td><\/tr>
ZELMAT Mohammed<\/td>Doc.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Associ\u00e9s<\/h2>\n\n\n\n
BELOUCHRANI Adel<\/td>Pr.<\/td><\/tr>
LUQUE Jean-Gabriel<\/td>Pr.<\/td><\/tr>
RACHIDI Mustapha<\/td>Pr.<\/td><\/tr>
SCHMID Wolfgang<\/td>Pr.<\/td><\/tr>
SZALAY L\u00e1szl\u00f3<\/td>Pr.<\/td><\/tr>
ZIADI Djelloul<\/td>Pr.<\/td><\/tr>
Dubernar Jean-Phillipe<\/td>MCA<\/td><\/tr>
NEMETH L\u00e1szl\u00f3<\/td>MCA<\/td><\/tr>
AMROUN Hamid<\/td>MCB<\/td><\/tr>
MIGNOT Ludovic<\/td>MCB<\/td><\/tr>
RAMIREZ Jos\u00e9-Luis<\/td>MCB<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n

Objectif et Comp\u00e9tences<\/h2>\n\n\n\n

L\u2019\u00e9quipe a des travaux engag\u00e9s dans les th\u00e9matiques suivantes, certaines sont en perspectives :<\/p>\n\n\n\n

\n
    \n
  • Combinatoire alg\u00e9brique ;<\/li>\n\n\n\n
  • Combinatoire \u00e9num\u00e9rative ;<\/li>\n\n\n\n
  • Th\u00e9orie ergodique ;<\/li>\n\n\n\n
  • Th\u00e9orie de l\u2019information ;<\/li>\n\n\n\n
  • Fonctions arithm\u00e9tiques ;<\/li>\n\n\n\n
  • Calcul quantique ;<\/li>\n\n\n\n
  • Coloration de graphes ;<\/li>\n\n\n\n
  • Th\u00e9orie des invariants ;<\/li>\n\n\n\n
  • Informatique th\u00e9orique ;<\/li>\n\n\n\n
  • Hypermatrices et hyperd\u00e9terminants ;<\/li>\n\n\n\n
  • Corr\u00e9lation mutuelle (statistique) ;<\/li>\n\n\n\n
  • Econom\u00e9trie des variables qualitatives ;<\/li>\n\n\n\n
  • Insertion professionnelle ;<\/li>\n\n\n\n
  • Contr\u00f4le statistique de qualit\u00e9 ;<\/li>\n\n\n\n
  • Plan d\u2019\u00e9chantillonnage (statistique).<\/li>\n<\/ul>\n<\/blockquote>\n\n\n\n
    \n\n\n\n

    Projets de Recherche<\/h2>\n\n\n\n

    L’\u00e9quipe participe aux projets scientifiques suivants.<\/p>\n\n\n\n

    CNEPRU : (en cours)<\/p>\n\n\n\n

    N\u00b0<\/th>C00L03UN 160420150019<\/td><\/tr>
    Intitul\u00e9<\/th>Combinatoire, dynamique et triangles arithm\u00e9tiques (CDTA)<\/td><\/tr>
    Responsable<\/th>Pr. BELBACHIR Hac\u00e8ne<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    PHC MAGHREB : (achev\u00e9)<\/p>\n\n\n\n

    N\u00b0<\/th>14MDU929<\/td><\/tr>
    Intitul\u00e9<\/th>Informatique Th\u00e9orique au Maghreb<\/td><\/tr>
    Responsable<\/th>Pr. Hac\u00e8ne BELBACHIR (USTHB, Alg\u00e9rie), Pr. J.-G. Luque (Rouen, France), Pr. I. Boudabous (Sfax, Tunisie) et Pr. O. Khadir (Mohammadia, Maroc)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    CNEPRU : (achev\u00e9)<\/p>\n\n\n\n

    N\u00b0<\/th>B01820120100<\/td><\/tr>
    Intitul\u00e9<\/th>Courbes et surfaces dans les 3-vari\u00e9t\u00e9s homog\u00e8nes. Quelques questions en th\u00e9orie des nombresque et triangles arithm\u00e9tiques (CDTA)<\/td><\/tr>
    Responsable<\/th>Pr. BOUYAKOUB Abdelkader<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    CNEPRU : (achev\u00e9)<\/p>\n\n\n\n

    N\u00b0<\/th>B00220120006<\/td><\/tr>
    Intitul\u00e9<\/th>Econom\u00e9trie, probabilit\u00e9s et combinatoire<\/td><\/tr>
    Responsable<\/th>Pr. HAMDI Fay\u00e7al<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    PNR : (achev\u00e9)<\/p>\n\n\n\n

    Agence<\/th>ATRST (ex ANDRU)<\/td><\/tr>
    N\u00b0<\/th>8\/u160\/664<\/td><\/tr>
    Intitul\u00e9<\/th>Suites R\u00e9currentes Lin\u00e9aires : Propri\u00e9t\u00e9s Arithm\u00e9tiques, Combinatoires et Probabilistes<\/td><\/tr>
    Responsable<\/th>Pr. BELBACHIR Hac\u00e8ne<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    PNR : (achev\u00e9)<\/p>\n\n\n\n

    Agence<\/th>ATRST (ex ANDRU)<\/td><\/tr>
    N\u00b0<\/th>8\/u160\/722<\/td><\/tr>
    Intitul\u00e9<\/th>Combinatoire et Arithm\u00e9tique de suites Remarquables et Applications<\/td><\/tr>
    Responsable<\/th>Pr. BENZAGHOU Benali<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

    CMEP\/TASSILI : (achev\u00e9)<\/p>\n\n\n\n

    N\u00b0<\/th>09MDU765<\/td><\/tr>
    Intitul\u00e9<\/th>Interactions entre l\u2019informatique th\u00e9orique et la combinatoire<\/td><\/tr>
    Responsable<\/th>Pr. BELBACHIR Hac\u00e8ne et Pr. J.-G Luque (Rouen, France)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
    \n\n\n\n

    Production<\/h2>\n\n\n\n

    La principale production scientifique de l’\u00e9quipe pour les ann\u00e9es 2013-2018 est :<\/p>\n\n\n\n

    Publications dans des revues :<\/u><\/strong><\/p>\n\n\n\n

    \n
      \n
    1. Hacene Belbachir<\/strong>, Nassira Souddi and Meriem Tigane. Combinatorial properties of the r-Whitney numbers of Dowling lattices. Ars Combinatoria, to appear, accepted in 2018.<\/li>\n\n\n\n
    2. R. Bellal<\/strong>, E. Lamini<\/strong>, H. Belbachir<\/strong>, S. Tagzout, A. Belouchrani. Improved Affine Arithmetic based Precision Analysis for Polynomial Function Evaluation. IEEE Transaction on Computers. Accepted 2018, DOI :10.1109\/TC.2018.2882537.<\/li>\n\n\n\n
    3. J.-L. Ram\u00edrez, H. Belbachir<\/strong>, C. Forero. The Generalized t-Comtet Numbers and Some Combinatorial Applications. Miskolc Mathematical Notes. To appear.<\/li>\n\n\n\n
    4. H. Belbachir<\/strong>, S. Hadj-Brahim<\/strong>. Some explicit formulas for Euler-Genocchi polynomials. \u00e0 paraitre dans INTEGERS.<\/li>\n\n\n\n
    5. A. F. Tebtoub<\/strong>. Log-concavity of principal diagonal rays in the regular Lah triangle. Ars Combinatoria, 2018, 75-83.<\/li>\n\n\n\n
    6. H. Belbachir<\/strong>, A. Belkhir<\/strong>. On some generalizations of Horadam numbers. Filomat, (14) 32, 2018.<\/li>\n\n\n\n
    7. H. Belbachir<\/strong>, S. Hadj-Brahim<\/strong>, M. Rachidi. On another approach for a family of Appell polynomials. 2018, (12) 32.<\/li>\n\n\n\n
    8. M. Ahmia<\/strong>, H. Belbachir<\/strong>. p,q-analogue of a linear transformation preserving log-convexity. Indian J. Pure Appl. Math., 2018, 49(3): 549-557.<\/li>\n\n\n\n
    9. M. Ahmia<\/strong>, H. Belbachir<\/strong>. The Log-concavity Property Associated to Hyperjacobsthal and Hyperjacobsthal-Lucas Sequences, Turkish Journal of Analysis and Number Theory, 2018, 6(3), 107-110.<\/li>\n\n\n\n
    10. M. Abchiche, H. Belbachir<\/strong>. Generalized Chebyshev polynomials. Discuss. Math. Gen. Algebra Appl. 38 (2018), no. 1, 79\u201389.<\/li>\n\n\n\n
    11. A. Bazeniar, M. Ahmia<\/strong>, H. Belbachir<\/strong>. Connection between bisnomial coefficients and their analogs and symmetric functions. Turkish J. Math. 42 (2018), no. 3, 807\u2013818.<\/li>\n\n\n\n
    12. L. Ait-Amrane, H. Belbachir<\/strong>. Periods of tribonacci sequences and elliptic curves. Algebra Discrete Math. 25 (2018), no. 1, 1\u201317.<\/li>\n\n\n\n
    13. H. Belbachir<\/strong>, M. A. Boutiche, A. Medjerredine<\/strong>. Enumerating some stable partitions involving Stirling and r-Stirling numbers of the second kind. Mediterr. J. Math. 15 (2018), no. 3, Art. 87, 12 pp.<\/li>\n\n\n\n
    14. M. Ahmia<\/strong>, H. Belbachir<\/strong>. Unimodality polynomials and generalized Pascal triangles. Algebra Discrete Math. 26 (2018), no. 1, 1\u20137.<\/li>\n\n\n\n
    15. E.-S. Lamini<\/strong>, S. Tagzout, H. Belbachir<\/strong>, A. Belouchrani. Precision analysis with analytical bit-width optimisation process for linear circuits with feedbacks. IET Circuits, Devices & Systems, vol. 12, no. 5, pp. 563\u2013570, 2018.<\/li>\n\n\n\n
    16. Kahina Amara, Oualid Djekoune, Nouara Achour, Mahmoud Belhocine & Rima Narimene Bellal<\/strong>. A Combined 2D\u20133D Object Detection Framework. IETE JOURNAL OF RESEARCH 63(5), 2017, pp. 607-615. <\/li>\n\n\n\n
    17. H. Belbachir<\/strong> and H. Harik<\/strong> ; Link between Hosoya index and Fibonacci numbers. Miskolc Mathematical Notes. To appear. <\/li>\n\n\n\n
    18. H. Belbachir<\/strong> and A. F. Tebtoub<\/strong> ; The t-successive associated Stirling numbers, t-Fibonacci-Stirling numbers and unimodality, Turkish Journal of Mathematics, 41(5) (2017), pp. 1279-1291. <\/li>\n\n\n\n
    19. H. Belbachir<\/strong> and L. Szalay ; Fibonacci and Lucas Pascal triangle, Hacettepe Journal of Mathematics and Statistics, 45(5) (2017), 1343-1354. <\/li>\n\n\n\n
    20. H. Belbachir<\/strong> and E. Kilic ; Generalized double binomial sums families by generating functions. Utilitas Mathematica, 104 (2017), pp. 161-174. <\/li>\n\n\n\n
    21. H. Belbachir<\/strong> and M. Mihoubi ; Identities related to integer partitions and complete Bell polynomials, Algebra and Discrete Mathematics, 24(1), (2017), 146-156. <\/li>\n\n\n\n
    22. H. Belbachir<\/strong>, H. Harik<\/strong> and S. Pirzada ; Determining Lucas identities by using Hosoya index, Creative Math. & Info. 26 (2017), N\u00b02, 145-151. <\/li>\n\n\n\n
    23. H. Belbachir<\/strong>, L. Nemeth and L. Szalay. Properties of hyperbolic Pascal triangles, AIP Conf. Proceeding, 1867, 020031, (2017), 1-5.<\/li>\n\n\n\n
    24. M. Ahmia<\/strong> and L. Szalay. On the weighted sums associated to rays in generalized Pascal triangle. Indian Journal of Discrete Mathematics, 1:8\u201317, 2016.<\/li>\n\n\n\n
    25. H. Belbachir<\/strong>, L. Ait-Amrane, K. Betina, Periods of Morgan-Voyce sequences and elliptic curves, to appear in Math. Slovaca 66 (2016), no. 6.<\/li>\n\n\n\n
    26. I. E. Bousbaa<\/strong>, A. Chouria, J. Luque. A combinatorial Hopf algebra for the boson normal ordering problem. Annales de l’Institut Henri Poincar\u00e9 D. http:\/\/www.ems-ph.org\/journals\/forthcoming.php?jrn=aihpd<\/li>\n\n\n\n
    27. H. Belbachir<\/strong>, L. Nemeth and L. Szalay. Hyperbolic Pascal triangles. Applied Mathematics and Computation, Volume: 273 (2016), 453-464.<\/li>\n\n\n\n
    28. H. Belbachir<\/strong> et A. Belkhir<\/strong>. On generalized Hyper-Fibonacci and incomplete Fibonacci polynomials in arithmetic progressions. Siauliai Math. Semin., Volume: 11 (19), 1-12, 2016.<\/li>\n\n\n\n
    29. H. Belbachir<\/strong>, M. Mihoubi. The (exponential) multipartitional polynomials and polynomial sequences of multinomial type, Part II. Arab J. Math. Sci 21 (2015), no. 1, 2\u201314.<\/li>\n\n\n\n
    30. H. Belbachir<\/strong>, A.-F. Tebtoub<\/strong>. Les nombres de Stirling associ\u00e9s avec succession d’ordre 2, nombres de Fibonacci\u2013Stirling et unimodalit\u00e9. C. R. Math. Acad. Sci. Paris 353 (2015), no. 9, 767\u2013771.<\/li>\n\n\n\n
    31. M. Abchiche, H. Belbachir<\/strong>. Generalized Lucas\u2019 Theorem. Ars Combin., 120, (2015) 413-416.<\/li>\n\n\n\n
    32. H. Belbachir<\/strong>, M. Mihoubi. Linear Recurrences for r-Bell Polynomials. J. Integer Seq. 17 (2014), Article 14.10.6, 10 pp.<\/li>\n\n\n\n
    33. H. Belbachir<\/strong>, T. Komatsu, L. Szalay. Linear recurrences associated to rays in Pascal\u2019s triangle and combinatorial identities, Math. Slovaca 64 (2014), no. 2, 287\u2013300.<\/li>\n\n\n\n
    34. H. Belbachir<\/strong>, I. E. Bousbaa<\/strong>. Combinatorial identities for the r-Lah numbers, Ars Combin., 115, (2014), 453-458.<\/li>\n\n\n\n
    35. H. Belbachir<\/strong>, At. Benmezai<\/strong>. A q-analogue for bi-s-nomial coefficients and generalized Fibonacci sequences. Comptes rendus – Math\u00e9matique 352 (2014) , n\u00b03, pp. 167-171.<\/li>\n\n\n\n
    36. H. Belbachir<\/strong>, At. Benmezai<\/strong>. An alternative approach to Cigler\u2019s q-Lucas polynomials. Applied Mathematics and Computation, 226 (2014), 691–698.<\/li>\n\n\n\n
    37. M. Ahmia<\/strong>, H. Belbachir<\/strong>, A. Belkhir<\/strong>. The log-concavity and log-convexity properties associated to hyperpell numbers and hyperpell-Lucas numbers, Ann. Math. Inform. 42 (2014).<\/li>\n\n\n\n
    38. D. Berkane<\/strong>. An explicit estimate for the Barban and Vehov weights. Notes on Number Theory and Discrete Mathematics, 20, 2014, No. 2, 35\u201343.<\/li>\n\n\n\n
    39. H. Belbachir<\/strong>, M. Mihoubi. The (exponential) multipartitional polynomials and polynomial sequences of multinomial type, Part I, Arab J. Math. Sci. 20 (2014), no. 2, 233\u2013245.<\/li>\n\n\n\n
    40. H. Belbachir<\/strong>, L. Szalay. Balancing in direction $(1,-1)$ in Pascal’s triangle. Armen. J. Math. 6 (2014), no. 1, 32\u201340.<\/li>\n\n\n\n
    41. H. Belbachir<\/strong>, L. Szalay. On the arithmetic triangles. Siauliai Math. Semin., 9 (17), 2014, 15-26.<\/li>\n\n\n\n
    42. H. Belbachir<\/strong>, A. Belkhir<\/strong>. Combinatorial expressions involving Fibonacci, hyperfibonacci and incomplete Fibonacci numbers. J. Integer Seq. 17 (2014), Article 14.4.3, 7 pp.<\/li>\n\n\n\n
    43. H. Belbachir<\/strong>, M. Rahmani. On Gessel-Kaneko\u2019s identity for Bernoulli numbers. Appl. Anal. Discrete Math. 7 (2013), 1\u201310. (appendix by I. M. Gessel).<\/li>\n\n\n\n
    44. H. Belbachir<\/strong>, A. Belkhir<\/strong>. Cross recurrence relations for r-Lah numbers, Ars Combin., 110, (2013) 199-203.<\/li>\n\n\n\n
    45. H. Belbachir<\/strong>, F. Bencherif. Sums of products of generalized Fibonacci and Lucas numbers, Ars Combin., 110, (2013) 33-43.<\/li>\n\n\n\n
    46. H. Belbachir<\/strong>, I. E. Bousbaa<\/strong>. Translated Whitney and r-Whitney Numbers: A Combinatorial Approach, J. Integer Seq. 16 (2013), Article 13.8.6, 7 pp.<\/li>\n\n\n\n
    47. H. Belbachir<\/strong>, A. Belkhir<\/strong>. Tiling approach to obtain identities for generalized Fibonacci and Lucas numbers, Ann. Math. Inform. 41 (2013), 13-17.<\/li>\n\n\n\n
    48. H. Belbachir<\/strong>, M. Mihoubi. Generalization of Universal Partition and Bipartition’s Theorems, Integers 13 (2013), A59, 11 pp.<\/li>\n<\/ol>\n<\/blockquote>\n\n\n\n

      Communications internationales :<\/u><\/strong><\/p>\n\n\n\n

      \n
        \n
      1. Samira Attou<\/strong>, Ludovic Mignot, Djelloul Ziadi. The Bottom-Up Position Tree Automaton and Its Compact Version. Implementation and Application of Automata – 23rd International Conference, CIAA 2018, Charlottetown, PE, Canada, July 30 – August 2, 2018. Proceedings. Lecture Notes in Computer Science 10977, Springer 2018, ISBN 978-3-319-94811-9, p. 59-70.<\/li>\n\n\n\n
      2. Beno\u00eet Rittaud, Pierre Audin, Hac\u00e8ne Belbachir<\/strong>, Pierre-Alain Cherix, Shaula Fiorelli Vilmart, Robin Jamet et Christian Mercat. Un avenant au contrat didactique : la vulgarisation en classe. EMF 2018, Paris, 22-26 octobre 2018.<\/li>\n\n\n\n
      3. Shaula Fiorelli Vilmart, Pierre Audin, Hac\u00e8ne Belbachir<\/strong>, France Caron, Pierre-Alain Cherix, Robin Jamet, Christian Mercat et Beno\u00eet Rittaud. Regards sur les ateliers r\u00e9cr\u00e9atifs. EMF 2018, Paris, 22-26 octobre 2018.<\/li>\n\n\n\n
      4. H. Belbachir<\/strong>. Extended classical inequalities according to hyperdeterminant. ICOT 2018 : International Conference on Operator Theory, April 30 – May 03, 2018, Hammamet, Tunisia.<\/li>\n\n\n\n
      5. H. Belbachir<\/strong>. Extended Genocchi-Euler polynomials, Bernoulli-Euler polynomials and Eulerian polynomials. ICAAM 2018 : International Conference on Advances in Applied Mathematics, December 17-20, 2018, Sousse, Tunisia.<\/li>\n\n\n\n
      6. Merabtine, N., Djenouri, D., Zegour, E., Lamini, R.<\/strong>, Bellal, R.<\/strong>, Ghaoui, I., & Dahlal, N. One-step clustering protocol for periodic traffic wireless sensor networks. Wireless and Optical Communication Conference (WOCC), April 7-8, 2017, New Jersey, USA, pp. 1-6. <\/li>\n\n\n\n
      7. H. Belbachir<\/strong>. 18\u00e8me salon Culture et Jeux Math\u00e9matiques, 27-30 mai 2017, Place Saint Sulpice \u00e0 Paris VI. <\/li>\n\n\n\n
      8. H. Belbachir<\/strong>. Multidimensional Gram inequality and multiple correlation coefficient. ICAAM 2017 : International Conference on Advances in Applied Mathematics, December 18-27, 2017, Hammamet, Tunisia.<\/li>\n\n\n\n
      9. H. Belbachir<\/strong>. Combinatorial and arithmetic properties for class of Appel polynomials. Journ\u00e9es Structures Discr\u00e8tes : Rouen, 27-29 Septembre 2017.<\/li>\n\n\n\n
      10. H. Belbachir<\/strong>. Hyperdeterminantal representation of Fibonacci sequences. LICMA\u201917, Libanese International Conference on Mathematics and Applications, Beirut, 16-19 mai 2017.<\/li>\n\n\n\n
      11. I. Benrabia<\/strong>. Bi\u00b2nomial coefficient analogues related to Fibonacci sequence. LICMA\u201917, Libanese International Conference on Mathematics and Applications, Beirut, 16-19 mai 2017.<\/li>\n\n\n\n
      12. H. Belbachir<\/strong>. Traitement des donn\u00e9es en TIC. A3SPA\u20192017 , Algerian Summer School on Signal Processing and its Applications : ‘Signal Processing for Telecommunications’, 17-20 December 2017, Guelma, Algeria.<\/li>\n\n\n\n
      13. N. Tahir, M. Boudraa ,A. A. El Ouchdi and E. Lamini<\/strong>. Implementation of cosine function used in Discrete Cosine Transform for computing MFCC Coefficient. International Conference on Technological Advances in Electrical Engineering (ICTAEE\u201916), October 2016, Skikda, Algerie. <\/li>\n\n\n\n
      14. A. Medjerredine<\/strong>. Combinatorial approach via Stirling numbers for some families of graphs. Conf\u00e9rence internationale et \u00e9cole d\u2019\u00e9t\u00e9 AEC\u201916, Linz, Autriche, 2016.<\/li>\n\n\n\n
      15. I. Benrabia<\/strong>. Combinatorial interpretation of binomial coefficient analogues related to 3-Fibonacci sequence. Conf\u00e9rence internationale et \u00e9cole d\u2019\u00e9t\u00e9 AEC\u201916, Linz, Autriche, 2016.<\/li>\n\n\n\n
      16. A. F. Tebtoub<\/strong>. Unimodality of diagonal rays in second kind\u2019s Stirling triangle. Conf\u00e9rence internationale et \u00e9cole d\u2019\u00e9t\u00e9 AEC\u201916, Linz, Autriche, 2016.<\/li>\n\n\n\n
      17. H. Belbachir<\/strong>. Une promenade parcourant le triangle de Pascal, la suite de Fibonacci, l\u2019hypercube, le cube de Fibonacci et l\u2019hyperd\u00e9terminant. 11eme Nuit de la science- Les r\u00e8gles du jeu, Gen\u00e8ve 9-10 juillet 2016.<\/li>\n\n\n\n
      18. H. Belbachir<\/strong>. Hyperdeterminants over hypercubes and hypergrids, Gauss’s composition Law, Lagrange identity and Gram inequality. ICAAM 2015, International Conference on Advances in Applied Mathematics, December 21-24, 2015, Hammamet, Tunisia.<\/li>\n\n\n\n
      19. Lamini E.-S.<\/strong>, Bellal R.<\/strong>, Belbachir H.<\/strong>, Tagzout S., Belouchrani A. Enhanced bit-width optimization for linear circuits with feedbacks, Proceedings of the 9th International Design and Test Symposium, IDT 2014, 7038607, pp. 168-173, (2015).<\/li>\n\n\n\n
      20. H. Belbachir<\/strong>, At. Benmezai<\/strong> et A. Bouyakoub, Chu-Vandermonde identity for q-analogue and p,q-analogue of bi-s-nomial coefficients. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19 Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      21. H. Belbachir , A. Mehdaoui et A. Belkhir<\/strong>, : The Stirling Numbers with constraint. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19 Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      22. H. Belbachir , A. Medjerredine<\/strong>, Associated Stirling numbers for some families of graphs. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19 Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      23. H. Belbachir,  I. E. Bousbaa et A. Belkhir<\/strong>, The Generalized r-Lah Numbers Revisited. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      24. H. Belbachir,  I. Benrabia<\/strong>, Tiling interpretation for combinatorial identity associated to order three Fibonacci sequence. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      25. H. Belbachir,  A. Belkhir<\/strong>, Statistic on linear tilings and generalized q-Fibonacci polynomials. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015, Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      26. H. Belbachir,  O. Igueroufa<\/strong>, Central Bisnomial Coefficients on Hypergrids. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      27. H. Belbachir,  S. Amrouche<\/strong>, Triangles arithm\u00e9tiques associ\u00e9es aux suites de Fibonacci g\u00e9n\u00e9ralis\u00e9es. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      28. H. Belbachir,  A. F. Tebtoub<\/strong>, The 2-successive Eulerian numbers and unimodality. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      29. I. E. Bousbaa<\/strong> et A. Chouria, The boson normal ordering problem : combinatorial interpretation. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      30. M. Ahmia<\/strong> et L. Szalay, On the weighted sums associated to rays of Pascal\u2019s triangle. DIMACOS\u201915, Conf\u00e9rence school on Discrete Mathematics and Computer Science 2015, 15-19  Novembre 2015., Sidi Bel Abb\u00e8s, Alg\u00e9rie.<\/li>\n\n\n\n
      31. H. Belbachir,  I. E. Bousbaa<\/strong> Associate r-Stirling numbers. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      32. H. Belbachir<\/strong> F. Krim, Linear recurrence associated to rays of negatively extended Pascal triangle. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      33. H. Belbachir,  A. Belkhir<\/strong> Some identities for the bivariate hyperfibonacci polynomials. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      34. H. Belbachir,  A. Tebtoub<\/strong>, Successive associated Stirling numbers. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      35. H. Belbachir,  A. Medjredine<\/strong> , A. Boutiche, Stirling and Bell numbers of some join graphs. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      36. H. Belbachir,  At. Benmezai<\/strong>, The q-analogue of Fibonacci and Lucas sequences. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      37. M. Ahmia,  H. Belbachir<\/strong> Unimodal rays in the q-bi-s-nomial coefficients. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      38. H. Belbachir , O. Igueroufa<\/strong>, Generalized Catalan numbers based on generalized Pascal triangle. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      39. H. Belbachir , H. Harik<\/strong>, On bandwidth of n-dimensional grid. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      40. H. Belbachir,  E. S. Lamini<\/strong>, S. Tagzout, A. Belouchrani, Optimisation de la largeur bit pour l\u2019optimisation des polyn\u00f4mes. ORPA\u20192015, Operational Research Practice in Africa, Alger USTHB) 20-22 Avril 2015.<\/li>\n\n\n\n
      41. H. Belbachir, H. Harik<\/strong>. On Fibonacci number identities. RAMA9, Rencontre d\u2019Analyse Math\u00e9matiques et ses Applications, 05-07 mai 2014, Laghouat.<\/li>\n\n\n\n
      42. H. Belbachir,  I. E. Bousbaa<\/strong>. Les nombres de Whitney et r-Whitney translates. RAMA9, Rencontre d\u2019Analyse Math\u00e9matiques et ses Applications, 05-07 mai 2014, Laghouat.<\/li>\n\n\n\n
      43. M. Ahmia, H. Belbachir<\/strong>. Properties of log-concavity and log-convexity associated to hyperpell and hyperpell- lucas numbers. RAMA9, Rencontre d\u2019Analyse Math\u00e9matiques et ses Applications, 05-07 mai 2014, Laghouat.<\/li>\n\n\n\n
      44. H. Belbachir,  E. Lamini<\/strong>. R. Bellal<\/strong>, S. Tagzout, A. Belouchrani, Enhanced Bit-Width Optimization for Linear Circuits with Feedbacks. IDT\u201914, 9th IEEE International Design & Test Symposium, 16-18 d\u00e9cembre 2014.<\/li>\n\n\n\n
      45. H. Belbachir, A. Belkhir<\/strong>. Combinatorial interpretation for hyperfibonacci numbers. RAMA9, Rencontre d\u2019Analyse Math\u00e9matiques et ses Applications, 05-07 mai 2014, Laghouat.<\/li>\n\n\n\n
      46. H. Belbachir<\/strong>, A. Boutiche. Merrifield-Simmons and Hosoya index of some thorny graphs. RAMA9, Rencontre d\u2019Analyse Math\u00e9matiques et ses Applications, 05-07 mai 2014, Laghouat.<\/li>\n\n\n\n
      47. At. Benmezai<\/strong>. Les q-analogues des suites de Fibonacci et de Lucas, une alternative aux approches de Carlitz et Cigler. Colloque international du LM2I, 08-12 d\u00e9cembre 2014, Lumini, CIRM.<\/li>\n\n\n\n
      48. H. Belbachir<\/strong>, s\u00e9minaire \u00ab Combinatoire et Algorithme \u00bb, d\u00e9cembre 2013, Universit\u00e9 de Rouen, LITIS. Titre : Les nombres de Whitney translat\u00e9s.<\/li>\n\n\n\n
      49. Belbachir, H., Harik<\/strong>, A., Cheurfi, S. Haboussi, F.<\/strong> and Taibi, W<\/strong>. Scientometric analysis of researche activity in Algerian university. International conference on scientometrics: status and prospects for development, 10-12 October 2013, Moscow.<\/li>\n\n\n\n
      50. Belbachir, H. and Harik<\/strong>, A. hg-index: an indicator to characterize research quality of academic researchers. International conference on scientometrics: status and prospects for development, 10-12 October 2013, Moscow.<\/li>\n<\/ol>\n<\/blockquote>\n\n\n\n

        Soutenances de th\u00e8ses :<\/u><\/strong><\/p>\n\n\n\n

        \n
          \n
        1. Es-seddik LAMINI<\/strong>. Arithm\u00e9tiques et algorithmiques pour l\u2019optimisation des circuits int\u00e9gr\u00e9s. Doctorat en Recherche Op\u00e9rationnelle et Math\u00e9matiques Discr\u00e8tes, soutenue le 08 novembre 2018 \u00e0 l\u2019USTHB ; Directeur de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne<\/strong>.<\/li>\n\n\n\n
        2. Assia MEDJERREDINE<\/strong>. Combinatorial interpretations of classical sequences in graphs. Doctorat en Recherche Op\u00e9rationnelle et Math\u00e9matiques Discr\u00e8tes, soutenue le 10 septembre 2018 \u00e0 l\u2019USTHB. Directeur de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne<\/strong>.<\/li>\n\n\n\n
        3. Amine BELKHIR.<\/strong> Combinatoire bijective des pavages et des partitions. Doctorat en Math\u00e9matiques, soutenue le 23 octobre 2016 \u00e0 l\u2019USTHB. Directeur de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne.<\/strong><\/li>\n\n\n\n
        4. BOUSBAA Imad Eddine<\/strong>.  Combinatoire des suites de Stirling g\u00e9n\u00e9ralis\u00e9es. Doctorat en Recherche Op\u00e9rationnelle et Math\u00e9matiques Discr\u00e8tes, soutenue le 18 juin 2016. Directeur de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne<\/strong>.<\/li>\n\n\n\n
        5. TEBTOUB Fettouma<\/strong>. Aspects combinatoires li\u00e9s \u00e0 la monotonie des suites classiques. Doctorat en Recherche Op\u00e9rationnelle et Math\u00e9matiques Discr\u00e8tes, soutenue le 31 mai 2016. Directeur de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne<\/strong>.<\/li>\n\n\n\n
        6. BENMEZAI Athmane.<\/strong> Le q-analogue des suites de Fibonacci et de Lucas. Doctorat en Math\u00e9matiques, soutenue le 25 mai 2016 \u00e0 l\u2019Universit\u00e9 d\u2019Oran 1. Co-directeurs de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne <\/strong>et Pr. BOUYAKOUB Abdelkader.<\/li>\n\n\n\n
        7. AHMIA Moussa<\/strong>. Log-concavit\u00e9, log-convexit\u00e9 et unimodalit\u00e9 des suites num\u00e9riques. Doctorat en recherche op\u00e9rationnelle soutenue le 12 juin 2015. Directeur de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne<\/strong>.<\/li>\n\n\n\n
        8. RAHMANI Mourad. Etude combinatoire et analytique des suites et des polyn\u00f4mes. Doctorat en recherche op\u00e9rationnelle soutenue le 08 d\u00e9cembre 2013. Directeur de th\u00e8se : Pr. BELBACHIR Hac\u00e8ne<\/strong>.<\/li>\n<\/ol>\n<\/blockquote>\n\n\n\n

          Habilitation :<\/u><\/strong><\/p>\n\n\n\n

          \n
            \n
          1. AHMIA Moussa<\/strong>. Soutenue le 08 12 2018 \u00e0 l\u2019universit\u00e9 de Jijel<\/li>\n\n\n\n
          2. BERKANE Djamel<\/strong>, Valeurs moyennes de quelques fonctions arithm\u00e9tiques, Habilitation en Math\u00e9matiques, soutenue \u00e0 Blida, le 19 Mai 2016.<\/li>\n<\/ol>\n<\/blockquote>\n\n\n\n

            Les membres de l’\u00e9quipe ont particip\u00e9 aussi \u00e0 de nombreuses publications nationales, communications nationales, soutenances de master et de licence et d’organisation de manifestations scientifiques nationales et internationales.<\/strong><\/p>\n\n\n\n

            <\/p>\n","protected":false},"excerpt":{"rendered":"

            Equipe Combinatoire, Arithm\u00e9tique et Informatique Th\u00e9orique (CATI) Responsable Pr. BELBACHIR Hac\u00e8ne Mail hbelbachir@usthb.dz Pr\u00e9sentation La th\u00e9matique de l\u2019\u00e9quipe se r\u00e9partie sur trois volets.Un volet, relatif \u00e0 la combinatoire, s\u2019articule autour de deux axes. Le premier s\u2019int\u00e9resse \u00e0 la combinatoire \u00e9num\u00e9rative Continue Reading<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":16,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-41","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/pages\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/comments?post=41"}],"version-history":[{"count":17,"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/pages\/41\/revisions"}],"predecessor-version":[{"id":353,"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/pages\/41\/revisions\/353"}],"up":[{"embeddable":true,"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/pages\/16"}],"wp:attachment":[{"href":"https:\/\/lrecits.usthb.dz\/index.php\/wp-json\/wp\/v2\/media?parent=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}