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On the Schaper Numbers of Partitions

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Jolliffe, Liam 
Martin, Stuart 

Abstract

One of the most useful tools for calculating the decomposition numbers of the symmetric group is Schaper’s sum formula [10]. The utility of this formula for a given Specht module can be improved by knowing the Schaper number of the corresponding partition. Fayers [2] gives a characterisation of those partitions whose Schaper number is at least two. In this paper we shall demonstrate how this knowledge can be used to calculate some decomposition numbers before extending this result with the hope of allowing more decomposition numbers to be calculated in the future. For p = 2 we shall give a complete characterisation of partitions whose Schaper number is at least three, and those whose Schaper number at least four. We also present a list of necessary conditions for a partition to have Schaper number at least three for odd primes and a conjecture on the sufficiency of these conditions

Description

Keywords

4901 Applied Mathematics, 4904 Pure Mathematics, 49 Mathematical Sciences

Journal Title

The Quarterly Journal Of Mathematics

Conference Name

Journal ISSN

0033-5606
1464-3847

Volume Title

Publisher

Oxford University Press (OUP)

Rights

All rights reserved