2007/09/04 by Yuliy Baryshnikov, Baryshnikov, Yuliy, Dan Romik +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Combinatorial Mathematics #Random Matrices and Applications
paper · pdf · doi:10.48550/arxiv.0709.0498
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.