Young diagram

Young tableau

A Young tableau is a Young diagram with numbers in each of the boxes. comb

[2][3]  [1][3][4]
[1][4], [5][2],     &c.

The normal Young tableau has these numbers in ascending order, and is hence unique for each numeric partition/Young diagram. comb

[1][2]  [1][2][3]
[3][4], [4][5],     &c.

A standard Young tableau has ascending columns and rows, hence the normal Young tableau is standard. comb Below are the only normal Young tableaux for

[1][2]  [1][3]
[3],    [2]

We denote the normal young diagram of as , whereas the result of permuting the boxes with is .

Properties

• The number of standard Young tableaux of shape is given by the Hook length formula

Further terminology and notation

• A young tableau in absolute value brackets denotes the product of its cells.
• A Semi-standard Young tableau has ascending columns and non-decreasing rows.

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