Refining overlined parts in overpartitions via residue classes: Bijections, generating functions, and congruences

Augustine O. Munagi, James A. Sellers

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Over the past several years, numerous authors have studied properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In this paper, we consider various classes of overpartitions where the "overlined parts" belong to certain residue classes modulo a positive integer m. We state new identities between such restricted overpartitions and standard partition functions. Finally, we prove a number of Ramanujan-like congruences for many of the restricted overpartition functions using elementary generating function manipulations.

Original languageEnglish (US)
Pages (from-to)33-49
Number of pages17
JournalUtilitas Mathematica
Volume95
StatePublished - Nov 1 2014
Externally publishedYes

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