Congruences from $q$-Catalan Identities

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2016Publisher:University of Isfahan, Department of Mathematics, IsfahanJournal:Transactions on Combinatorics (issn: 2251-8657,

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Authors: Zou, Qing;

doi: 10.22108/toc.2016.20358

Congruences from $q$-Catalan Identities

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Abstract

Summary: In this paper, by studying three $q$-Catalan identities given by Andrews, we arrive at a certain number of congruences. These congruences are all modulo $\Phi_n(q)$, the $n$-th cyclotomic polynomial or the related functions and modulo $q$-integers.

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University of Iowa
United States

Keywords

congruences, ‎Catalan numbers‎, ‎$q$-Catalan identities‎, Binomial coefficients; factorials; $q$-identities, $q$-integer, ‎$q$-integer‎, QA1-939, ‎Cyclotomic polynomial, Congruences; primitive roots; residue systems, cyclotomic polynomial, $q$-Catalan identities, Catalan numbers, Factorials, binomial coefficients, combinatorial functions, ‎Congruences‎, Mathematics, Combinatorial identities, bijective combinatorics

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