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 language | English |
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Article number | #80 |
Journal | Seminaire Lotharingien de Combinatoire |
Issue number | 86 |
State | Published - 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.
Funders | Funder number |
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MIT-Israel | |
Bar-Ilan University | |
Israel Science Foundation | 1970/18 |
Nemzeti Kutatási Fejlesztési és Innovációs Hivatal | 138596 |
Keywords
- conjugacy class
- cyclic descent
- higher Lie character
- symmetric group