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arXiv · 1701.07077

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

I. P. Goulden·Pavel Shuldiner
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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 $m$

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I. P. Goulden, Pavel Shuldiner. 2017-01-24. Characterizing the number of coloured $m$-ary partitions modulo $m$, with and without gaps. https://arxiv.org/abs/1701.07077

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