English

Enumeration formulas for Young tableaux in a diagonal strip

Combinatorics 2007-09-05 v1

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.

Keywords

Cite

@article{arxiv.0709.0498,
  title  = {Enumeration formulas for Young tableaux in a diagonal strip},
  author = {Yuliy Baryshnikov and Dan Romik},
  journal= {arXiv preprint arXiv:0709.0498},
  year   = {2007}
}

Comments

32 pages, 8 figures

R2 v1 2026-06-21T09:13:51.037Z