Descents of $\lambda$-unimodal cycles in a character formula

Kassie Archer

Descents of $\lambda$-unimodal cycles in a character formula

Combinatorics 2016-06-07 v3

Authors: Kassie Archer

Abstract

We prove an identity conjectured by Adin and Roichman involving the descent set of $\lambda$ -unimodal cyclic permutations. These permutations appear in formulas for characters of certain representations of the symmetric group. Such formulas have previously been proven algebraically. In this paper, we present a combinatorial proof for one such formula and discuss the consequences for the distribution of the descent set on cyclic permutations.

Keywords

$\lambda$-unimodal cyclic permutations descent set character formula symmetric group combinatorial proof

Cite

@article{arxiv.1401.2433,
  title  = {Descents of $\lambda$-unimodal cycles in a character formula},
  author = {Kassie Archer},
  journal= {arXiv preprint arXiv:1401.2433},
  year   = {2016}
}

Comments

16 pages, 1 figure

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