Dans cet article, nous introduisons des modèles combinatoires pour les analogues en plusieurs variables des polynômes de Bernoulli et des nombres d’Euler de deux types. Comme application, nous donnons des preuves combinatoires de certaines identités faisant intervenir les polynômes de Bernoulli généralisés.
In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.
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Mots clés : Poly-Bernoulli polynomial, poly-Euler number
@article{JTNB_2022__34_3_917_0,
author = {B\'enyi, Be\'ata and Matsusaka, Toshiki},
title = {Combinatorial aspects of {poly-Bernoulli} polynomials and {poly-Euler} numbers},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {917--939},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {34},
number = {3},
year = {2022},
doi = {10.5802/jtnb.1234},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.1234/}
}
TY - JOUR AU - Bényi, Beáta AU - Matsusaka, Toshiki TI - Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers JO - Journal de théorie des nombres de Bordeaux PY - 2022 SP - 917 EP - 939 VL - 34 IS - 3 PB - Société Arithmétique de Bordeaux UR - http://www.numdam.org/articles/10.5802/jtnb.1234/ DO - 10.5802/jtnb.1234 LA - en ID - JTNB_2022__34_3_917_0 ER -
%0 Journal Article %A Bényi, Beáta %A Matsusaka, Toshiki %T Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers %J Journal de théorie des nombres de Bordeaux %D 2022 %P 917-939 %V 34 %N 3 %I Société Arithmétique de Bordeaux %U http://www.numdam.org/articles/10.5802/jtnb.1234/ %R 10.5802/jtnb.1234 %G en %F JTNB_2022__34_3_917_0
Bényi, Beáta; Matsusaka, Toshiki. Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers. Journal de théorie des nombres de Bordeaux, Tome 34 (2022) no. 3, pp. 917-939. doi : 10.5802/jtnb.1234. http://www.numdam.org/articles/10.5802/jtnb.1234/
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