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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
##### Keywords:
partitions; $$m$$-ary partitions; congruence properties
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