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] => [2,3,1] => [[1,2],[3]] => [[2,1,0],[2,0],[1]] => 4
[1,0,1,1,0,0] => [2,1,3] => [[1,3],[2]] => [[2,1,0],[1,1],[1]] => 5
[1,1,0,0,1,0] => [1,3,2] => [[1,2],[3]] => [[2,1,0],[2,0],[1]] => 4
[1,1,0,1,0,0] => [3,1,2] => [[1,3],[2]] => [[2,1,0],[1,1],[1]] => 5
[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] => [2,3,4,1] => [[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 5
[1,0,1,0,1,1,0,0] => [2,3,1,4] => [[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => 6
[1,0,1,1,0,0,1,0] => [2,1,4,3] => [[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 7
[1,0,1,1,0,1,0,0] => [2,4,1,3] => [[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => 6
[1,0,1,1,1,0,0,0] => [2,1,3,4] => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
[1,1,0,0,1,0,1,0] => [1,3,4,2] => [[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 5
[1,1,0,0,1,1,0,0] => [1,3,2,4] => [[1,2,4],[3]] => [[3,1,0,0],[2,1,0],[2,0],[1]] => 6
[1,1,0,1,0,0,1,0] => [3,1,4,2] => [[1,3],[2,4]] => [[2,2,0,0],[2,1,0],[1,1],[1]] => 7
[1,1,0,1,0,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => [[2,2,0,0],[2,1,0],[2,0],[1]] => 6
[1,1,0,1,1,0,0,0] => [3,1,2,4] => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
[1,1,1,0,0,0,1,0] => [1,2,4,3] => [[1,2,3],[4]] => [[3,1,0,0],[3,0,0],[2,0],[1]] => 5
[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] => [4,1,2,3] => [[1,3,4],[2]] => [[3,1,0,0],[2,1,0],[1,1],[1]] => 7
[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 (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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.