Young tableau

Semi-standard Young tableau

A semi-standard Young tableau is a Young tableau with strictly increasing columns and strictly non-decreasing rows¹, comb as opposed to a standard Young tableau which in addition has strictly increasing rows.

[1][1]  [1][2]
[2]     [2]

Semi-standard Young tableaux of shape λ=(2,1) with cells less than 2

Properties

• The number of semi-standard Young tableaux with each cell is given by Stanley’s hook content formula.

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tidy | en | sembr

Footnotes

1. 2023, Groups and representations, §7.2.5, p. 109 ↩