Three different ways to obtain the values of hyper $m$-ary partition functions

Jiae Eom; Gyeonga Jeong; Jaebum Sohn

doi:10.4134/BKMS.b151039

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(6): 1857-1868

Online first article September 20, 2016 Printed November 30, 2016

https://doi.org/10.4134/BKMS.b151039

Three different ways to obtain the values of hyper $m$-ary partition functions

Jiae Eom, Gyeonga Jeong, and Jaebum Sohn

Yonsei University, Yonsei University, Yonsei University

Abstract

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Abstract

We consider a natural generalization of $ h_2 (n) $, denoted \linebreak $ h_m (n) $, which is the number of partitions of $n$ into parts which are power of $m \geq 2$ wherein each power of $m$ is allowed to be used as a part at most $m$ times. In this note, we approach in three different ways using the recurrences, the matrix and the tree to calculate the value of $h_m (n)$.

Keywords: hyper $m$-ary partition function, hyper $m$-ary tree

MSC numbers: Primary 05A17, 11P81