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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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https://hal.inria.fr/hal-01207601
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Submitted on : Thursday, October 1, 2015 - 9:29:06 AM
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### Citation

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, ⟨10.46298/dmtcs.2411⟩. ⟨hal-01207601⟩

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