J. Korean Math. Soc. 2017; 54(4): 1243-1264
Online first article December 29, 2016 Printed July 1, 2017
https://doi.org/10.4134/JKMS.j160448
Copyright © The Korean Mathematical Society.
Dae San Kim and Taekyun Kim
Sogang University, Kwangwoon University
In this paper, we introduce $w$-Catalan polynomials as a generalization of Catalan polynomials and derive fourteen basic identities of symmetry in three variables related to $w$-Catalan polynomials and analogues of alternating power sums. In addition, specializations of one of the variables as one give us new and interesting identities of symmetry even for two variables. The derivations of identities are based on the $p$-adic integral expression for the generating function of the $w$-Catalan polynomials and the quotient of $p$-adic integrals for that of the analogues of the alternating power sums.
Keywords: Catalan polynomial, $w$-Catalan polynomial, fermionic $p$-adic integral, identities of symmetry
MSC numbers: 11B83, 11S80, 05A19
2014; 51(5): 1045-1073
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