Descents of $\lambda$-unimodal cyclic permutations

We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combi...

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Bibliographic Details
Published in:Discrete mathematics and theoretical computer science 2014-01, Vol.DMTCS Proceedings vol. AT,... (Proceedings), p.417-428
Main Author: Archer, Kassie
Format: Article
Language:English
Subjects:
[info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
[math.math-co] mathematics [math]/combinatorics [math.co]
characters of representations of the symmetric group
Combinatorics
Computer Science
cyclic permutation
descent
Discrete Mathematics
Mathematics
necklaces
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Summary:We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$-unimodal cyclic permutations. These permutations appear in the character formulas for certain representations of the symmetric group and these formulas are usually proven algebraically. Here, we give a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations. Nous prouvons une identité conjecturée par Adin et Roichman impliquant les ensembles des descentes des permutations cycliques $\lambda$-unimodales. Ces permutations apparaissent dans les formules des caractères pour certaines représentations du groupe symétrique, et ces formules sont généralement prouvées dans une manière algébrique. Ici, nous donnons une preuve combinatoire pour une telle formule et discutons les conséquences pour la distribution de l’ensemble des descentes sur des permutations cycliques.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.2411