Identifier
Values
[[1]] => [1] => [1] => [1] => 0
[[1,2]] => [1,2] => [1,2] => [1,2] => 0
[[1],[2]] => [2,1] => [2,1] => [2,1] => 1
[[1,2,3]] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[[1,3],[2]] => [2,1,3] => [1,3,2] => [1,3,2] => 1
[[1,2],[3]] => [3,1,2] => [3,1,2] => [3,1,2] => 2
[[1],[2],[3]] => [3,2,1] => [3,2,1] => [3,2,1] => 2
[[1,2,3,4]] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[[1,3,4],[2]] => [2,1,3,4] => [1,3,2,4] => [1,3,2,4] => 1
[[1,2,4],[3]] => [3,1,2,4] => [1,3,4,2] => [1,3,4,2] => 2
[[1,2,3],[4]] => [4,1,2,3] => [4,1,3,2] => [4,1,3,2] => 3
[[1,3],[2,4]] => [2,4,1,3] => [3,1,2,4] => [3,1,2,4] => 2
[[1,2],[3,4]] => [3,4,1,2] => [3,1,4,2] => [3,1,4,2] => 3
[[1,4],[2],[3]] => [3,2,1,4] => [1,4,3,2] => [1,4,3,2] => 2
[[1,3],[2],[4]] => [4,2,1,3] => [4,2,3,1] => [4,2,3,1] => 4
[[1,2],[3],[4]] => [4,3,1,2] => [4,2,1,3] => [4,2,1,3] => 3
[[1],[2],[3],[4]] => [4,3,2,1] => [4,3,1,2] => [4,3,1,2] => 3
[[1,2,3,4,5]] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
[[1,3,4,5],[2]] => [2,1,3,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
[[1,2,4,5],[3]] => [3,1,2,4,5] => [1,3,4,2,5] => [1,3,4,2,5] => 2
[[1,2,3,5],[4]] => [4,1,2,3,5] => [1,3,4,5,2] => [1,3,4,5,2] => 3
[[1,3,5],[2,4]] => [2,4,1,3,5] => [1,4,2,5,3] => [1,4,2,5,3] => 3
[[1,2,5],[3,4]] => [3,4,1,2,5] => [1,4,5,2,3] => [1,4,5,2,3] => 4
[[1,4,5],[2],[3]] => [3,2,1,4,5] => [1,4,3,2,5] => [1,4,3,2,5] => 2
[[1,3,5],[2],[4]] => [4,2,1,3,5] => [1,4,3,5,2] => [1,4,3,5,2] => 3
[[1,2,5],[3],[4]] => [4,3,1,2,5] => [1,4,5,3,2] => [1,4,5,3,2] => 3
[[1,5],[2],[3],[4]] => [4,3,2,1,5] => [1,5,4,3,2] => [1,5,4,3,2] => 3
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Description
The number of Bruhat lower covers of a permutation.
This is, for a signed permutation $\pi$, the number of signed permutations $\tau$ having a reduced word which is obtained by deleting a letter from a reduced word from $\pi$.
Map
ones to leading
Description
The unique permutation obtained by applying the Foata-Riordan map to obtain a Prüfer code, then prepending zero and cyclically shifting.
Let $c_1,\dots, c_{n-1}$ be the Prüfer code obtained via the Foata-Riordan map described in [1, eq (1.2)] and let $c_0 = 0$.
This map returns the a unique permutation $q_1,\dots, q_n$ such that $q_i - c_{i-1}$ is constant modulo $n+1$.
This map is Mp00299ones to leading restricted to permutations.
Map
reading word permutation
Description
Return the permutation obtained by reading the entries of the tableau row by row, starting with the bottom-most row in English notation.
Map
to signed permutation
Description
The signed permutation with all signs positive.