Block inclusions and cores of partitions

Jørn B. Olsson; Dennis Stanton

doi:10.1007/s00010-006-2867-1

Block inclusions and cores of partitions

Jørn B. Olsson, Dennis Stanton

School of Mathematics

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

44 Scopus citations

Abstract

Necessary and sufficient conditions are given for an s-block of integer partitions to be contained in a t-block. The generating function for such partitions is found analytically, and also bijectively, using the notion of an (s, t)-abacus. The largest partition which is both an s-core and a t-core is explicitly given.

Original language	English (US)
Pages (from-to)	90-110
Number of pages	21
Journal	Aequationes Mathematicae
Volume	74
Issue number	1-2
DOIs	https://doi.org/10.1007/s00010-006-2867-1
State	Published - Sep 2007

Bibliographical note

Funding Information:
The first author was supported by the Danish National Research Council. was supported by NSF grant DMS-0503660.

Keywords

Blocks of partitions
Characters
Cores

Publisher link

10.1007/s00010-006-2867-1

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AB - Necessary and sufficient conditions are given for an s-block of integer partitions to be contained in a t-block. The generating function for such partitions is found analytically, and also bijectively, using the notion of an (s, t)-abacus. The largest partition which is both an s-core and a t-core is explicitly given.

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KW - Characters

KW - Cores

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Block inclusions and cores of partitions

Abstract

Bibliographical note

Keywords

Publisher link

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