On m-ary overpartitions

Øystein J. Rødseth; James A. Sellers

doi:10.1007/s00026-005-0262-6

On m-ary overpartitions

Øystein J. Rødseth, James A. Sellers

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Presently there are a lot of activities in the study of overpartitions, objects that were discussed by MacMahon, and which have recently proven useful in several combinatorial studies of basic hypergeometric series. In this paper we study some similar objects, which we name m-ary overpartitions. We consider divisibility properties of the number of m-ary overpartitions of a natural number, and we prove a theorem which is a lifting to general m of the well-known Churchhouse congruences for the binary partition function.

Original language	English (US)
Pages (from-to)	345-353
Number of pages	9
Journal	Annals of Combinatorics
Volume	9
Issue number	3
DOIs	https://doi.org/10.1007/s00026-005-0262-6
State	Published - Oct 1 2005
Externally published	Yes

Keywords

Generating function
Overpartition
Partition
m-ary overpartition

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10.1007/s00026-005-0262-6

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AU - Sellers, James A.

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AB - Presently there are a lot of activities in the study of overpartitions, objects that were discussed by MacMahon, and which have recently proven useful in several combinatorial studies of basic hypergeometric series. In this paper we study some similar objects, which we name m-ary overpartitions. We consider divisibility properties of the number of m-ary overpartitions of a natural number, and we prove a theorem which is a lifting to general m of the well-known Churchhouse congruences for the binary partition function.

KW - Generating function

KW - Overpartition

KW - Partition

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On m-ary overpartitions

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Keywords

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