Higher Lie Characters and Cyclic Descent Extension on Conjugacy Classes

Ron M. Adin, Pál Hegedüs, Yuval Roichman

Research output: Contribution to journalArticlepeer-review

Abstract

A now-classical cyclic extension of the descent set of a permutation has been introduced by Klyachko and Cellini. Following a recent axiomatic approach to this notion, it is natural to ask which sets of permutations admit such a (not necessarily classical) extension. The main result of this paper is a complete answer in the case of conjugacy classes of permutations. It is shown that the conjugacy class of cycle type λ has such an extension if and only if λ is not of the form (rs) for some square-free r. The proof involves a detailed study of hook constituents in higher Lie characters.

Original languageEnglish
Article number#80
JournalSeminaire Lotharingien de Combinatoire
Issue number86
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022, Seminaire Lotharingien de Combinatoire. All Rights Reserved.

Funding

*[email protected]. Partially supported by the Israel Science Foundation grant no. 1970/18 and by an MIT-Israel MISTI grant. †[email protected]. Partially supported by Hungarian National Research, Development and Innovation Office (NKFIH) grant no. 138596 and by a Bar-Ilan University visiting grant. ‡[email protected]. Partially supported by the Israel Science Foundation grant no. 1970/18 and by an MIT-Israel MISTI grant.

FundersFunder number
MIT-Israel
Bar-Ilan University
Israel Science Foundation1970/18
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal138596

    Keywords

    • conjugacy class
    • cyclic descent
    • higher Lie character
    • symmetric group

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