Processing math: 100%

Identifier
Values
[1] => [1,0,1,0] => [[1,3],[2,4]] => [2,2] => 0
[2] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,3] => 0
[1,1] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,3,1] => 3
[2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,2,2] => 0
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Description
The absolute variation of a composition.
Map
valley composition
Description
The composition corresponding to the valley set of a standard tableau.
Let T be a standard tableau of size n.
An entry i of T is a descent if i+1 is in a lower row (in English notation), otherwise i is an ascent.
An entry 2in1 is a valley if i1 is a descent and i is an ascent.
This map returns the composition c1,,ck of n such that {c1,c1+c2,,c1++ck} is the valley set of T.
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.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.