Characterizing the number of coloured m-ary partitions modulo m, with and without gaps

2017/01/24 by I. P. Goulden, Goulden, I. P., Pavel Shuldiner +1
Mathematics · #05A15 #05A17 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1701.07077

openalex publication_date 2017/01/24 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In a pair of recent papers, Andrews, Fraenkel and Sellers provide a complete characterization for the number of m-ary partitions modulo m, with and without gaps. In this paper we extend these results to the case of coloured m-ary partitions, with and without gaps. Our method of proof is different, giving explicit expansions for the generating functions modulo m

Related

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• On the Enumeration and Congruences for m-ary Partitions
• General Congruences Modulo 5 and 7 for Colour Partitions
• Congruences on the Number of Restricted m-ary Partitions
• Computerizing the Andrews-Fraenkel-Sellers Proofs on the Number of m-ary partitions mod m (and doing MUCH more!)