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Descents of $\lambda$-unimodal cyclic permutations

Abstract : 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.
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Kassie Archer. Descents of $\lambda$-unimodal cyclic permutations. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.417-428. ⟨hal-01207601⟩

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