• Corpus ID: 119639959

Enumeration of Standard Young Tableaux

@article{Adin2014EnumerationOS,
  title={Enumeration of Standard Young Tableaux},
  author={Ron M. Adin and Yuval Roichman},
  journal={arXiv: Combinatorics},
  year={2014}
}

• R. Adin, Yuval Roichman
• Published 19 August 2014
• Mathematics
• arXiv: Combinatorics

Question 1.1. What is the total number of resulting configurations? How many configurations are there of any particular shape? In order to answer these questions, at least partially, recall the symmetric group Sn of all permutations of the numbers 1, . . . , n. An involution is a permutation π ∈ Sn such that π is the identity permutation. Theorem 1.2. The total number of configurations of n balls is equal to the number of involutions in the symmetric group Sn. Theorem 1.2 may be traced back to Frobenius and Schur. A combinatorial proof will be outlined in Section 4 (see Corollary 4.12). Example 1.3. There are four configurations on three balls. Indeed, {π ∈ S3 : π = 1} = {123, 132, 213, 321}.