The distribution of the number of parts of m-ary partitions modulo m

2016/02/29 by Edgar, Tom · 1 citation
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.00085

Abstract

We investigate the number of parts modulo m of m-ary partitions of a positive integer n. We prove that the number of parts is equidistributed modulo m on a special subset of m-ary partitions. As consequences, we explain when the number of parts is equidistributed modulo m on the entire set of partitions, and we provide an alternate proof of a recent result of Andrews, Fraenkel, and Sellers about the number of m-ary partitions modulo m.

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• Rectangle partitions generalizing integer partitions

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