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arXiv · 0709.0498

Enumeration formulas for Young tableaux in a diagonal strip

Yuliy Baryshnikov·Dan Romik
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Abstract

We derive combinatorial identities, involving the Bernoulli and Euler numbers, for the numbers of standard Young tableaux of certain skew shapes. This generalizes the classical formulas of D. Andre on the number of up-down permutations. The analysis uses a transfer operator approach extending the method of Elkies, combined with an identity expressing the volume of a certain polytope in terms of a Schur function.

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Yuliy Baryshnikov, Dan Romik. 2007-09-04. Enumeration formulas for Young tableaux in a diagonal strip. https://arxiv.org/abs/0709.0498

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