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.
All Science Journal Classification (ASJC) codes
- Control and Optimization
- Computational Mathematics
- Computational Theory and Mathematics