# Minimal and maximal constituents of twisted Foulkes characters

Paget, Rowena E., Wildon, Mark (2014) Minimal and maximal constituents of twisted Foulkes characters. Journal of the London Mathematical Society, 93 (2). pp. 301-318. ISSN 0024-6107. (doi:10.1112/jlms/jdv070)

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http://dx.doi.org/10.1112/jlms/jdv070

## Abstract

We prove combinatorial rules that give the minimal and maximal partitions labelling the irreducible constituents of a family of characters for the symmetric group that generalize Foulkes permutation characters. Restated in the language of symmetric functions, our results determine all minimal and maximal partitions that label Schur functions appearing in the plethysms $s_\nu \circ s_{(m)}$. As a corollary we prove two conjectures of Agaoka on the lexicographically least constituents of the plethysms $s_\nu \circ s_{(m)}$ and $s_\nu \circ s_{(1^m)}$.

Item Type: Article 10.1112/jlms/jdv070 Q Science > QA Mathematics (inc Computing science) > QA165 Combinatorics Q Science > QA Mathematics (inc Computing science) > QA171 Representation theory Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Rowena E Paget 14 Oct 2014 09:42 UTC 29 May 2019 13:12 UTC https://kar.kent.ac.uk/id/eprint/43385 (The current URI for this page, for reference purposes)