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Young tableau

The Young tableau (plural, "tableaux") of a Ferrers diagram is obtained by placing the numbers 1, ..., in the 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 are given by , , , and , illustrated above. The bumping algorithm is used to construct a standard Young tableau from a permutation of , 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 relationwith 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..

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