On the enumeration of skew Young tableaux

Authors:
R. P. Stanley
Affiliations:
-
Venue:
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Year:
2003

Citing 2
Cited 2

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Skew domino Schensted correspondence and sign-imbalance

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Abstract

For fixed n and a fixed partition α of k we give an explicit formula for the number N(n; α) of standard skew Young tableaux with n squares and shape λ/α for some λ. From this formula the entire asymptotic expansion of N(n; α) as n → ∞ can in principle be computed, generalizing recent work of McKay, Morse, and Wilf. We also give asymptotic formulas for the number fλ/α of standard skew Young tableaux of shape λ/α for α fixed and λ "large."