On the Enumeration of Skew Young Tableaux

Richard P. Stanley

On the Enumeration of Skew Young Tableaux

Combinatorics 2007-05-23 v2

Authors: Richard P. Stanley

Abstract

We extend work of McKay, Morse, and Wilf by giving exact formulas and asymptotic formulas for the number of skew Young tableaux T in two situations: (1) the "inside shape" and total number of cells of T are fixed, and (2) the inside shape of T is fixed. The proofs use the theory of symmetric functions and estimates for irreducible characters of the symmetric group due to Thoma, Vershik, Kerov, and Biane.

Keywords

skew young tableaux enumeration symmetric functions irreducible characters symmetric group asymptotic formula

Cite

@article{arxiv.math/0106115,
  title  = {On the Enumeration of Skew Young Tableaux},
  author = {Richard P. Stanley},
  journal= {arXiv preprint arXiv:math/0106115},
  year   = {2007}
}

Comments

15 pages; a few typos corrected

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