- FindStat

Identifier

Mp00075: Semistandard tableaux —reading word permutation⟶ Permutations
St000209: Permutations ⟶ ℤ

Values

[[1,2]] => [1,2] => 0

[[2,2]] => [1,2] => 0

[[1],[2]] => [2,1] => 1

[[1,3]] => [1,2] => 0

[[2,3]] => [1,2] => 0

[[3,3]] => [1,2] => 0

[[1],[3]] => [2,1] => 1

[[2],[3]] => [2,1] => 1

[[1,1,2]] => [1,2,3] => 0

[[1,2,2]] => [1,2,3] => 0

[[2,2,2]] => [1,2,3] => 0

[[1,1],[2]] => [3,1,2] => 2

[[1,2],[2]] => [2,1,3] => 1

[[1,4]] => [1,2] => 0

[[2,4]] => [1,2] => 0

[[3,4]] => [1,2] => 0

[[4,4]] => [1,2] => 0

[[1],[4]] => [2,1] => 1

[[2],[4]] => [2,1] => 1

[[3],[4]] => [2,1] => 1

[[1,1,3]] => [1,2,3] => 0

[[1,2,3]] => [1,2,3] => 0

[[1,3,3]] => [1,2,3] => 0

[[2,2,3]] => [1,2,3] => 0

[[2,3,3]] => [1,2,3] => 0

[[3,3,3]] => [1,2,3] => 0

[[1,1],[3]] => [3,1,2] => 2

[[1,2],[3]] => [3,1,2] => 2

[[1,3],[2]] => [2,1,3] => 1

[[1,3],[3]] => [2,1,3] => 1

[[2,2],[3]] => [3,1,2] => 2

[[2,3],[3]] => [2,1,3] => 1

[[1],[2],[3]] => [3,2,1] => 2

[[1,1,1,2]] => [1,2,3,4] => 0

[[1,1,2,2]] => [1,2,3,4] => 0

[[1,2,2,2]] => [1,2,3,4] => 0

[[2,2,2,2]] => [1,2,3,4] => 0

[[1,1,1],[2]] => [4,1,2,3] => 3

[[1,1,2],[2]] => [3,1,2,4] => 2

[[1,2,2],[2]] => [2,1,3,4] => 1

[[1,1],[2,2]] => [3,4,1,2] => 2

[[1,5]] => [1,2] => 0

[[2,5]] => [1,2] => 0

[[3,5]] => [1,2] => 0

[[4,5]] => [1,2] => 0

[[5,5]] => [1,2] => 0

[[1],[5]] => [2,1] => 1

[[2],[5]] => [2,1] => 1

[[3],[5]] => [2,1] => 1

[[4],[5]] => [2,1] => 1

[[1,1,4]] => [1,2,3] => 0

[[1,2,4]] => [1,2,3] => 0

[[1,3,4]] => [1,2,3] => 0

[[1,4,4]] => [1,2,3] => 0

[[2,2,4]] => [1,2,3] => 0

[[2,3,4]] => [1,2,3] => 0

[[2,4,4]] => [1,2,3] => 0

[[3,3,4]] => [1,2,3] => 0

[[3,4,4]] => [1,2,3] => 0

[[4,4,4]] => [1,2,3] => 0

[[1,1],[4]] => [3,1,2] => 2

[[1,2],[4]] => [3,1,2] => 2

[[1,4],[2]] => [2,1,3] => 1

[[1,3],[4]] => [3,1,2] => 2

[[1,4],[3]] => [2,1,3] => 1

[[1,4],[4]] => [2,1,3] => 1

[[2,2],[4]] => [3,1,2] => 2

[[2,3],[4]] => [3,1,2] => 2

[[2,4],[3]] => [2,1,3] => 1

[[2,4],[4]] => [2,1,3] => 1

[[3,3],[4]] => [3,1,2] => 2

[[3,4],[4]] => [2,1,3] => 1

[[1],[2],[4]] => [3,2,1] => 2

[[1],[3],[4]] => [3,2,1] => 2

[[2],[3],[4]] => [3,2,1] => 2

[[1,1,1,3]] => [1,2,3,4] => 0

[[1,1,2,3]] => [1,2,3,4] => 0

[[1,1,3,3]] => [1,2,3,4] => 0

[[1,2,2,3]] => [1,2,3,4] => 0

[[1,2,3,3]] => [1,2,3,4] => 0

[[1,3,3,3]] => [1,2,3,4] => 0

[[2,2,2,3]] => [1,2,3,4] => 0

[[2,2,3,3]] => [1,2,3,4] => 0

[[2,3,3,3]] => [1,2,3,4] => 0

[[3,3,3,3]] => [1,2,3,4] => 0

[[1,1,1],[3]] => [4,1,2,3] => 3

[[1,1,2],[3]] => [4,1,2,3] => 3

[[1,1,3],[2]] => [3,1,2,4] => 2

[[1,1,3],[3]] => [3,1,2,4] => 2

[[1,2,2],[3]] => [4,1,2,3] => 3

[[1,2,3],[2]] => [2,1,3,4] => 1

[[1,2,3],[3]] => [3,1,2,4] => 2

[[1,3,3],[2]] => [2,1,3,4] => 1

[[1,3,3],[3]] => [2,1,3,4] => 1

[[2,2,2],[3]] => [4,1,2,3] => 3

[[2,2,3],[3]] => [3,1,2,4] => 2

[[2,3,3],[3]] => [2,1,3,4] => 1

[[1,1],[2,3]] => [3,4,1,2] => 2

[[1,1],[3,3]] => [3,4,1,2] => 2

[[1,2],[2,3]] => [2,4,1,3] => 3

[[1,2],[3,3]] => [3,4,1,2] => 2

>>> Load all 2284 entries. <<<

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Description

Maximum difference of elements in cycles.
Given a cycle $C$ in a permutation, we can compute the maximum distance between elements in the cycle, that is $\max \{ a_i-a_j | a_i, a_j \in C \}$.
The statistic is then the maximum of this value over all cycles in the permutation.

Map

reading word permutation

Description

Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottommost row (in English notation).