Séminaire Lotharingien de Combinatoire, 86B.80 (2022), 12 pp.
Ron M. Adin, Pál Hegedüs and Yuval Roichman
Higher Lie Characters and Cyclic Descent Extension on Conjugacy Classes
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.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
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