Identifier
Values
[1] => [1,0,1,0] => [[1,3],[2,4]] => [2,4,1,3] => 2
[2] => [1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [3,4,6,1,2,5] => 2
[1,1] => [1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [2,5,6,1,3,4] => 2
[2,1] => [1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [2,4,6,1,3,5] => 4
search for individual values
searching the database for the individual values of this statistic
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searching the database for statistics with the same generating function
Description
The number of big ascents of a permutation.
For a permutation $\pi$, this is the number of indices $i$ such that $\pi(i+1)−\pi(i) > 1$.
For the number of small ascents, see St000441The number of successions of 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.
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 Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.