Identifier
Values
[1] => [[1],[]] => 1
[1,1] => [[1,1],[]] => 1
[2] => [[2],[]] => 1
[1,1,1] => [[1,1,1],[]] => 1
[1,2] => [[2,1],[]] => 2
[2,1] => [[2,2],[1]] => 2
[3] => [[3],[]] => 1
[1,1,1,1] => [[1,1,1,1],[]] => 1
[1,1,2] => [[2,1,1],[]] => 3
[1,2,1] => [[2,2,1],[1]] => 5
[1,3] => [[3,1],[]] => 3
[2,1,1] => [[2,2,2],[1,1]] => 3
[2,2] => [[3,2],[1]] => 5
[3,1] => [[3,3],[2]] => 3
[4] => [[4],[]] => 1
[1,1,1,1,1] => [[1,1,1,1,1],[]] => 1
[1,1,1,2] => [[2,1,1,1],[]] => 4
[1,1,2,1] => [[2,2,1,1],[1]] => 9
[1,1,3] => [[3,1,1],[]] => 6
[1,2,1,1] => [[2,2,2,1],[1,1]] => 9
[1,2,2] => [[3,2,1],[1]] => 16
[1,3,1] => [[3,3,1],[2]] => 11
[1,4] => [[4,1],[]] => 4
[2,1,1,1] => [[2,2,2,2],[1,1,1]] => 4
[2,1,2] => [[3,2,2],[1,1]] => 11
[2,2,1] => [[3,3,2],[2,1]] => 16
[2,3] => [[4,2],[1]] => 9
[3,1,1] => [[3,3,3],[2,2]] => 6
[3,2] => [[4,3],[2]] => 9
[4,1] => [[4,4],[3]] => 4
[5] => [[5],[]] => 1
[1,1,1,1,1,1] => [[1,1,1,1,1,1],[]] => 1
[1,1,1,1,2] => [[2,1,1,1,1],[]] => 5
[1,1,1,2,1] => [[2,2,1,1,1],[1]] => 14
[1,1,1,3] => [[3,1,1,1],[]] => 10
[1,1,2,1,1] => [[2,2,2,1,1],[1,1]] => 19
[1,1,2,2] => [[3,2,1,1],[1]] => 35
[1,1,3,1] => [[3,3,1,1],[2]] => 26
[1,1,4] => [[4,1,1],[]] => 10
[1,2,1,1,1] => [[2,2,2,2,1],[1,1,1]] => 14
[1,2,1,2] => [[3,2,2,1],[1,1]] => 40
[1,2,2,1] => [[3,3,2,1],[2,1]] => 61
[1,2,3] => [[4,2,1],[1]] => 35
[1,3,1,1] => [[3,3,3,1],[2,2]] => 26
[1,3,2] => [[4,3,1],[2]] => 40
[1,4,1] => [[4,4,1],[3]] => 19
[1,5] => [[5,1],[]] => 5
[2,1,1,1,1] => [[2,2,2,2,2],[1,1,1,1]] => 5
[2,1,1,2] => [[3,2,2,2],[1,1,1]] => 19
[2,1,2,1] => [[3,3,2,2],[2,1,1]] => 40
[2,1,3] => [[4,2,2],[1,1]] => 26
[2,2,1,1] => [[3,3,3,2],[2,2,1]] => 35
[2,2,2] => [[4,3,2],[2,1]] => 61
[2,3,1] => [[4,4,2],[3,1]] => 40
[2,4] => [[5,2],[1]] => 14
[3,1,1,1] => [[3,3,3,3],[2,2,2]] => 10
[3,1,2] => [[4,3,3],[2,2]] => 26
[3,2,1] => [[4,4,3],[3,2]] => 35
[3,3] => [[5,3],[2]] => 19
[4,1,1] => [[4,4,4],[3,3]] => 10
[4,2] => [[5,4],[3]] => 14
[5,1] => [[5,5],[4]] => 5
[6] => [[6],[]] => 1
[1,1,1,1,1,1,1] => [[1,1,1,1,1,1,1],[]] => 1
[1,1,1,1,1,2] => [[2,1,1,1,1,1],[]] => 6
[1,1,1,1,2,1] => [[2,2,1,1,1,1],[1]] => 20
[1,1,1,1,3] => [[3,1,1,1,1],[]] => 15
[1,1,1,2,1,1] => [[2,2,2,1,1,1],[1,1]] => 34
[1,1,1,2,2] => [[3,2,1,1,1],[1]] => 64
[1,1,1,3,1] => [[3,3,1,1,1],[2]] => 50
[1,1,1,4] => [[4,1,1,1],[]] => 20
[1,1,2,1,1,1] => [[2,2,2,2,1,1],[1,1,1]] => 34
[1,1,2,1,2] => [[3,2,2,1,1],[1,1]] => 99
[1,1,2,2,1] => [[3,3,2,1,1],[2,1]] => 155
[1,1,2,3] => [[4,2,1,1],[1]] => 90
[1,1,3,1,1] => [[3,3,3,1,1],[2,2]] => 71
[1,1,3,2] => [[4,3,1,1],[2]] => 111
[1,1,4,1] => [[4,4,1,1],[3]] => 55
[1,1,5] => [[5,1,1],[]] => 15
[1,2,1,1,1,1] => [[2,2,2,2,2,1],[1,1,1,1]] => 20
[1,2,1,1,2] => [[3,2,2,2,1],[1,1,1]] => 78
[1,2,1,2,1] => [[3,3,2,2,1],[2,1,1]] => 169
[1,2,1,3] => [[4,2,2,1],[1,1]] => 111
[1,2,2,1,1] => [[3,3,3,2,1],[2,2,1]] => 155
[1,2,2,2] => [[4,3,2,1],[2,1]] => 272
[1,2,3,1] => [[4,4,2,1],[3,1]] => 181
[1,2,4] => [[5,2,1],[1]] => 64
[1,3,1,1,1] => [[3,3,3,3,1],[2,2,2]] => 50
[1,3,1,2] => [[4,3,3,1],[2,2]] => 132
[1,3,2,1] => [[4,4,3,1],[3,2]] => 181
[1,3,3] => [[5,3,1],[2]] => 99
[1,4,1,1] => [[4,4,4,1],[3,3]] => 55
[1,4,2] => [[5,4,1],[3]] => 78
[1,5,1] => [[5,5,1],[4]] => 29
[1,6] => [[6,1],[]] => 6
[2,1,1,1,1,1] => [[2,2,2,2,2,2],[1,1,1,1,1]] => 6
[2,1,1,1,2] => [[3,2,2,2,2],[1,1,1,1]] => 29
[2,1,1,2,1] => [[3,3,2,2,2],[2,1,1,1]] => 78
[2,1,1,3] => [[4,2,2,2],[1,1,1]] => 55
[2,1,2,1,1] => [[3,3,3,2,2],[2,2,1,1]] => 99
[2,1,2,2] => [[4,3,2,2],[2,1,1]] => 181
>>> Load all 127 entries. <<<
[2,1,3,1] => [[4,4,2,2],[3,1,1]] => 132
[2,1,4] => [[5,2,2],[1,1]] => 50
[2,2,1,1,1] => [[3,3,3,3,2],[2,2,2,1]] => 64
[2,2,1,2] => [[4,3,3,2],[2,2,1]] => 181
[2,2,2,1] => [[4,4,3,2],[3,2,1]] => 272
[2,2,3] => [[5,3,2],[2,1]] => 155
[2,3,1,1] => [[4,4,4,2],[3,3,1]] => 111
[2,3,2] => [[5,4,2],[3,1]] => 169
[2,4,1] => [[5,5,2],[4,1]] => 78
[2,5] => [[6,2],[1]] => 20
[3,1,1,1,1] => [[3,3,3,3,3],[2,2,2,2]] => 15
[3,1,1,2] => [[4,3,3,3],[2,2,2]] => 55
[3,1,2,1] => [[4,4,3,3],[3,2,2]] => 111
[3,1,3] => [[5,3,3],[2,2]] => 71
[3,2,1,1] => [[4,4,4,3],[3,3,2]] => 90
[3,2,2] => [[5,4,3],[3,2]] => 155
[3,3,1] => [[5,5,3],[4,2]] => 99
[3,4] => [[6,3],[2]] => 34
[4,1,1,1] => [[4,4,4,4],[3,3,3]] => 20
[4,1,2] => [[5,4,4],[3,3]] => 50
[4,2,1] => [[5,5,4],[4,3]] => 64
[4,3] => [[6,4],[3]] => 34
[5,1,1] => [[5,5,5],[4,4]] => 15
[5,2] => [[6,5],[4]] => 20
[6,1] => [[6,6],[5]] => 6
[7] => [[7],[]] => 1
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
click to show known generating functions       
Description
The number of standard Young tableaux of the skew partition.
Map
to ribbon
Description
The ribbon shape corresponding to an integer composition.
For an integer composition $(a_1, \dots, a_n)$, this is the ribbon shape whose $i$th row from the bottom has $a_i$ cells.