Young tableau

Summary

A Young tableau is a Young diagram whose boxes are filled with positive integers, with the entries increasing along rows and down columns. In a standard tableau the entries are $1, \dots, n$, each used once; in a semistandard tableau repetitions are allowed along rows. Tableaux index bases of the irreducible representations of the symmetric group and of the general linear group. They are the combinatorial heart of Schur polynomials, the hook length formula and the Robinson–Schensted correspondence.