Arithmetic Properties of m-ary Partitions Without Gaps

George E. Andrews, Eduardo Brietzke, Øystein J. Rødseth, James Sellers

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Motivated by recent work of Bessenrodt, Olsson, and Sellers on unique path partitions, we consider partitions of an integer n wherein the parts are all powers of a fixed integer m≥ 2 and there are no "gaps" in the parts; that is, if mi is the largest part in a given partition, then mj also appears as a part in the partition for each 0 ≤ j< i. Our ultimate goal is to prove an infinite family of congruences modulo powers of m which are satisfied by these functions.

Original languageEnglish (US)
Pages (from-to)495-506
Number of pages12
JournalAnnals of Combinatorics
Issue number4
StatePublished - Dec 1 2017
Externally publishedYes


  • congruences
  • m-ary partitions
  • unique path partitions


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