A bijective proof of the hook-length formula |
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Authors: | D. S. Franzblau Doron Zeilberger |
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Affiliation: | Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 USA;Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel |
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Abstract: | A well-known theorem of Frame, Robinson, and, Thrall states that if λ is a partition of n, then the number of Standard Young Tableaux of shape λ 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 λ, and the set of pairs (T, S), where T is a Standard Young Tableau of shape λ and S is a “Pointer” Tableau of shape λ. |
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