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

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