On the Enumeration of Skew Young Tableaux

Details On the Enumeration of Skew Young Tableaux On the Enumeration of Skew Young Tableaux

2001-06-13

arxiv.org/abs/math/0106115v2

Mathematics

Combinatorics

15 pages; a few typos corrected

Scientific paper

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.

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