A bijective proof of the hook-length formula

D. S. Franzblau, Doron Zeilberger

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)317-343
Number of pages27
JournalJournal of Algorithms
Issue number4
StatePublished - Dec 1982
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Computational Theory and Mathematics


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