A bijective proof of the hook-length formula for skew shapes

نویسنده

Matjaz Konvalinka

چکیده

A well-known theorem of Frame, Robinson, and, Thrall states that if h is a partition of n, then the number of Standard Young Tableaux of shape h is n! divided by the product of the hook-lengths. We give a new combinatorial proof of this formula by exhibiting a bijection between the set of unsorted Young Tableaux of shape A, and the set of pairs (T, S), where T is a Standard Young Tableau of shape h and S is a “Pointer” Tableau of shape A.

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