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The distribution of the number of parts of \(m\)-ary partitions modulo \(m\). (English) Zbl 1376.05011
Summary: 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 G. E. Andrews et al. [Am. Math. Mon. 122, No. 9, 880–885 (2015; Zbl 1342.05013)] regarding the number of \(m\)-ary partitions modulo \(m\).

MSC:
05A17 Combinatorial aspects of partitions of integers
11P83 Partitions; congruences and congruential restrictions
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