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Descent Functions and Random Young Tableaux

Ron M. Adin·Yuval Roichman
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Abstract

The expectation of the descent number of a random Young tableau of a fixed shape is given, and concentration around the mean is shown. This result is generalized to the major index and to other descent functions. The proof combines probabilistic arguments together with combinatorial character theory. Connections with Hecke algebras are mentioned.

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Ron M. Adin, Yuval Roichman. 2000-11-05. Descent Functions and Random Young Tableaux. https://arxiv.org/abs/math/9910165

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