Identifier
-
Mp00199:
Dyck paths
—prime Dyck path⟶
Dyck paths
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St001130: Permutations ⟶ ℤ
Values
[1,0] => [1,1,0,0] => [[1,2],[3,4]] => [3,4,1,2] => 0
[1,0,1,0] => [1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [3,5,6,1,2,4] => 0
[1,1,0,0] => [1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [4,5,6,1,2,3] => 2
[] => [1,0] => [[1],[2]] => [2,1] => 0
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Description
The number of two successive successions in a permutation.
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
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
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
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