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Art of Computer Programming, The: Volume 3: Sorting and Searching by Donald E. Knuth

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*5.1.4. Tableaux and Involutions

To complete our survey of the combinatorial properties of permutations, we will discuss some remarkable relations that connect permutations with arrays of integers called tableaux. A Young tableau of shape (n1, n2, . . ., nm), where n1n2 ≥ · · · ≥ nm > 0, is an arrangement of n1 + n2 + · · · + nm distinct integers in an array of left-justified rows, with ni elements in row i, such that the entries of each row are in increasing order from left to right, and the entries of each column are increasing from top to bottom. For example,

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is a Young tableau of shape (6, 4, 4, 1). Such arrangements were introduced by ...

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