Identifier
Values
[1,0,1,0] => [2,1] => [[1],[2]] => [[1,1],[1]] => 3
[1,1,0,0] => [1,2] => [[1,2]] => [[2,0],[1]] => 2
[1,0,1,0,1,0] => [2,1,3] => [[1,3],[2]] => [[2,1,0],[1,1],[1]] => 5
[1,0,1,1,0,0] => [2,3,1] => [[1,2],[3]] => [[2,1,0],[2,0],[1]] => 4
[1,1,0,0,1,0] => [3,1,2] => [[1,3],[2]] => [[2,1,0],[1,1],[1]] => 5
[1,1,0,1,0,0] => [1,3,2] => [[1,2],[3]] => [[2,1,0],[2,0],[1]] => 4
[1,1,1,0,0,0] => [1,2,3] => [[1,2,3]] => [[3,0,0],[2,0],[1]] => 3
[1,0,1,0,1,0,1,0] => [2,1,4,3] => [[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 7
[1,0,1,0,1,1,0,0] => [2,4,1,3] => [[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => 6
[1,0,1,1,0,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
[1,0,1,1,0,1,0,0] => [2,3,1,4] => [[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => 6
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 5
[1,1,0,0,1,0,1,0] => [3,1,4,2] => [[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 7
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => 6
[1,1,0,1,0,0,1,0] => [3,1,2,4] => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
[1,1,0,1,0,1,0,0] => [1,3,2,4] => [[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => 6
[1,1,0,1,1,0,0,0] => [1,3,4,2] => [[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 5
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
[1,1,1,0,0,1,0,0] => [1,4,2,3] => [[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => 6
[1,1,1,0,1,0,0,0] => [1,2,4,3] => [[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 5
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [[1,2,3,4]] => [[4,0,0,0],[3,0,0],[2,0],[1]] => 4
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Description
The number of nonzero entries in a Gelfand Tsetlin pattern.
Map
to Gelfand-Tsetlin pattern
Description
Sends a tableau to its corresponding Gelfand-Tsetlin pattern.
To obtain this Gelfand-Tsetlin pattern, fill in the first row of the pattern with the shape of the tableau.
Then remove the maximal entry from the tableau to obtain a smaller tableau, and repeat the process until the tableau is empty.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding recording tableau.