standard tableau | tableau | Young diagram

The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., n in the n boxes of the diagram. A "standard" Young tableau is a Young tableau in which the numbers form an increasing sequence along each line and along each column. For example, the standard Young tableaux of size n = 3 are given by {{1, 2, 3}}, {{1, 3}, {2}}, {{1, 2}, {3}}, and {{1}, {2}, {3}}, illustrated above. The bumping algorithm is used to construct a standard Young tableau from a permutation of {1, ..., n}, and the number 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

bumping algorithm | Durfee square | Ferrers diagram | hook length formula | partition | partition function P | permutation involution | random tableau | Schensted correspondence | tableau class