Enumeration formulas for Young tableaux in a diagonal strip

Details Enumeration formulas for Young tableaux in a diagonal strip Enumeration formulas for Young tableaux in a diagonal strip

2007-09-04

arxiv.org/abs/0709.0498v1

Mathematics

Combinatorics

32 pages, 8 figures

Scientific paper

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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