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2017 The distribution of the number of parts of $m$-ary partitions modulo $m$
Tom Edgar
Rocky Mountain J. Math. 47(6): 1825-1838 (2017). DOI: 10.1216/RMJ-2017-47-6-1825

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 regarding the number of $m$-ary partitions modulo~$m$.

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Tom Edgar. "The distribution of the number of parts of $m$-ary partitions modulo $m$." Rocky Mountain J. Math. 47 (6) 1825 - 1838, 2017. https://doi.org/10.1216/RMJ-2017-47-6-1825

Information

Published: 2017
First available in Project Euclid: 21 November 2017

zbMATH: 1376.05011
MathSciNet: MR3725246
Digital Object Identifier: 10.1216/RMJ-2017-47-6-1825

Subjects:
Primary: 05A17, 11P83

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 6 • 2017
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