A Young tableau (plural, "tableaux") is a filling of the boxes of a Ferrers diagram with positive integers. A standard Young tableau with boxes contains each of 1, 2, ..., once, with entries increasing along each row and down each column. For example, the standard Young tableaux of size are given by , , , and , illustrated above. The bumping algorithm is used to construct a standard Young tableau from a permutation of , and the numbers of standard Young tableaux of size 1, 2, 3, ... are 1, 2, 4, 10, 26, 76, 232, 764, 2620, 9496, ... (OEIS A000085). These numbers can be generated by the recurrence relation

for integers , with and . This is the same as the number of permutation involutions on elements (Skiena 1990, p. 32).

The number of all possible standard Young tableaux of a given shape can also be considered, and can be calculated with the hook length formula. For example, the illustration above shows the 35 standard tableaux of shape .

The Schensted correspondence is a bijection between permutations of elements and pairs of standard Young tableaux of the same shape, each containing 1, 2, ..., once.

A semistandard Young tableau has entries weakly increasing along rows and strictly increasing down columns. Entries may repeat.