Comptes Rendus
no. 3
Combinatorics/Number theory
A q-analogue for bisnomial coefficients and generalized Fibonacci sequences
[Un q-analogue pour les coefficients bisnomiaux et les suites de Fibonacci généralisées]

Présenté par : the Editorial Board

Hacène Belbachir1 ; Athmane Benmezai2, 3
1 USTHB, Faculty of Mathematics, RECITS Laboratory, DG-RSDT, BP 32, El Alia 16111, Bab Ezzouar, Algiers, Algeria
2 University of Dely Brahim, Fac. of Eco. & Manag. Sc., RECITS Laboratory, DG-RSDT, Rue Ahmed Ouaked, Dely Brahim, Algiers, Algeria
3 University of Oran, Faculty of Sciences, BP 1524, ELM Naouer, 31000, Oran, Algeria
Comptes Rendus. Mathématique, Volume 352 (2014) no. 3, pp. 167-171.

Nous proposons une nouvelle variante de q-analogue pour les coefficients binomiaux généralisés appelés coefficients bisnomiaux. Elle est basée sur les suites q-Fibonacci proposées par Cigler.

A new q-analogue of bisnomial coefficients is proposed according to the generalized q-Fibonacci sequence suggested by Cigler's approach.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.01.009

Hacène Belbachir 1 ; Athmane Benmezai 2, 3

1 USTHB, Faculty of Mathematics, RECITS Laboratory, DG-RSDT, BP 32, El Alia 16111, Bab Ezzouar, Algiers, Algeria
2 University of Dely Brahim, Fac. of Eco. & Manag. Sc., RECITS Laboratory, DG-RSDT, Rue Ahmed Ouaked, Dely Brahim, Algiers, Algeria
3 University of Oran, Faculty of Sciences, BP 1524, ELM Naouer, 31000, Oran, Algeria 
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Hacène Belbachir; Athmane Benmezai. A q-analogue for bisnomial coefficients and generalized Fibonacci sequences. Comptes Rendus. Mathématique, Volume 352 (2014) no. 3, pp. 167-171. doi : 10.1016/j.crma.2014.01.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.01.009/

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  • Hacène Belbachir; Yassine Otmani Supercongruences concerning bisnomial coefficients, Rocky Mountain Journal of Mathematics, Volume 54 (2024) no. 4, pp. 943-953 | DOI:10.1216/rmj.2024.54.943 | Zbl:1550.11004
  • Hacène Belbachir; Toufik Djellal; Jean-Gabriel Luque On the self-convolution of generalized Fibonacci numbers, Quaestiones Mathematicae, Volume 46 (2023) no. 5, pp. 841-854 | DOI:10.2989/16073606.2022.2043949 | Zbl:1542.11025
  • Nassima Belaggoun; Hacène Belbachir; Athmane Benmezai A q-analogue of the bi-periodic Fibonacci and Lucas sequences and Rogers-Ramanujan identities, The Ramanujan Journal, Volume 60 (2023) no. 3, pp. 693-728 | DOI:10.1007/s11139-022-00647-4 | Zbl:1523.11028
  • Yousra Ghemit; Moussa Ahmia Overpartition analogues of q-bisnomial coefficients: basic properties and log-concavity, The Ramanujan Journal, Volume 62 (2023) no. 2, pp. 431-455 | DOI:10.1007/s11139-023-00706-4 | Zbl:1522.05013
  • Said Amrouche; Hacene Belbachir Asymmetric extension of Pascal-Delannoy triangles, Applicable Analysis and Discrete Mathematics, Volume 16 (2022) no. 2, pp. 328-349 | DOI:10.2298/aadm200411028a | Zbl:1513.11067
  • Abdelghafour Bazeniar; Moussa Ahmia; Abderrahmane Bouchair Log-concave sequences of bisnomial coefficients with their analogs and symmetric functions, Indian Journal of Pure Applied Mathematics, Volume 53 (2022) no. 1, pp. 127-137 | DOI:10.1007/s13226-021-00018-7 | Zbl:1483.05005
  • Moussa Ahmia; Boualam Rezig Two-Motzkin-like numbers and Stieltjes moment sequences, Mediterranean Journal of Mathematics, Volume 18 (2021) no. 2, p. 18 (Id/No 65) | DOI:10.1007/s00009-021-01700-0 | Zbl:1459.05345
  • Moussa Ahmia; Hacène Belbachir Log-concavity and LC-positivity for generalized triangles, Journal of Integer Sequences, Volume 23 (2020) no. 5, p. article | Zbl:1480.05015
  • Hacène Belbachir; Oussama Igueroufa Congruence properties for bisnomial coefficients and like extended Ram and Kummer theorems under suitable hypothesis, Mediterranean Journal of Mathematics, Volume 17 (2020) no. 1, p. 14 (Id/No 36) | DOI:10.1007/s00009-019-1457-0 | Zbl:1439.11056
  • Said Amrouche; Hacène Belbachir Unimodality and linear recurrences associated with rays in the Delannoy triangle, Turkish Journal of Mathematics, Volume 44 (2020) no. 1, pp. 118-130 | Zbl:1444.05005
  • Moussa Ahmia; Hacène Belbachir Preserving log-concavity for p,q-binomial coefficient, Discrete Mathematics, Algorithms and Applications, Volume 11 (2019) no. 2, p. 11 (Id/No 1950017) | DOI:10.1142/s1793830919500174 | Zbl:1410.05010
  • Moussa Ahmia; Hacène Belbachir Q-total positivity and strong q-log-convexity for some generalized triangular arrays, The Ramanujan Journal, Volume 49 (2019) no. 2, pp. 341-352 | DOI:10.1007/s11139-018-0102-z | Zbl:1416.05043
  • Abdelghafour Bazeniar; Moussa Ahmia; Hacene Belbachir Connection between bisnomial coefficients and their analogs and symmetric functions, Turkish Journal of Mathematics, Volume 42 (2018) no. 3, pp. 807-818 | DOI:10.3906/mat-1705-27 | Zbl:1424.05006
  • Xiaoli Ye; Zhizheng Zhang A common generalization of convolved generalized Fibonacci and Lucas polynomials and its applications, Applied Mathematics and Computation, Volume 306 (2017), pp. 31-37 | DOI:10.1016/j.amc.2017.02.016 | Zbl:1411.11018

Cité par 14 documents. Sources : zbMATH

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