Minimal and maximal constituents of twisted Foulkes characters

Rowena Paget, Mark Wildon

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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 $s_\nu \circ s_{(1^m)}$.
Original languageEnglish
Pages (from-to)301-318
Number of pages18
JournalJournal of the London Mathematical Society
Volume93
Issue number2
Early online date22 Jan 2016
DOIs
Publication statusPublished - Apr 2016

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