Identifier
Values
[1] => [1] => 10 => [1,2] => 1
[1,2] => [2] => 100 => [1,3] => 1
[2,1] => [1,1] => 110 => [1,1,2] => 1
[1,2,3] => [3] => 1000 => [1,4] => 1
[1,3,2] => [2,1] => 1010 => [1,2,2] => 1
[2,1,3] => [2,1] => 1010 => [1,2,2] => 1
[2,3,1] => [2,1] => 1010 => [1,2,2] => 1
[3,1,2] => [2,1] => 1010 => [1,2,2] => 1
[3,2,1] => [1,1,1] => 1110 => [1,1,1,2] => 1
[1,2,3,4] => [4] => 10000 => [1,5] => 1
[1,2,4,3] => [3,1] => 10010 => [1,3,2] => 1
[1,3,2,4] => [3,1] => 10010 => [1,3,2] => 1
[1,3,4,2] => [3,1] => 10010 => [1,3,2] => 1
[1,4,2,3] => [3,1] => 10010 => [1,3,2] => 1
[1,4,3,2] => [2,1,1] => 10110 => [1,2,1,2] => 1
[2,1,3,4] => [3,1] => 10010 => [1,3,2] => 1
[2,1,4,3] => [2,2] => 1100 => [1,1,3] => 1
[2,3,1,4] => [3,1] => 10010 => [1,3,2] => 1
[2,3,4,1] => [3,1] => 10010 => [1,3,2] => 1
[2,4,1,3] => [2,2] => 1100 => [1,1,3] => 1
[2,4,3,1] => [2,1,1] => 10110 => [1,2,1,2] => 1
[3,1,2,4] => [3,1] => 10010 => [1,3,2] => 1
[3,1,4,2] => [2,2] => 1100 => [1,1,3] => 1
[3,2,1,4] => [2,1,1] => 10110 => [1,2,1,2] => 1
[3,2,4,1] => [2,1,1] => 10110 => [1,2,1,2] => 1
[3,4,1,2] => [2,2] => 1100 => [1,1,3] => 1
[3,4,2,1] => [2,1,1] => 10110 => [1,2,1,2] => 1
[4,1,2,3] => [3,1] => 10010 => [1,3,2] => 1
[4,1,3,2] => [2,1,1] => 10110 => [1,2,1,2] => 1
[4,2,1,3] => [2,1,1] => 10110 => [1,2,1,2] => 1
[4,2,3,1] => [2,1,1] => 10110 => [1,2,1,2] => 1
[4,3,1,2] => [2,1,1] => 10110 => [1,2,1,2] => 1
[4,3,2,1] => [1,1,1,1] => 11110 => [1,1,1,1,2] => 1
[1,3,2,5,4] => [3,2] => 10100 => [1,2,3] => 1
[1,3,5,2,4] => [3,2] => 10100 => [1,2,3] => 1
[1,4,2,5,3] => [3,2] => 10100 => [1,2,3] => 1
[1,4,5,2,3] => [3,2] => 10100 => [1,2,3] => 1
[2,1,3,5,4] => [3,2] => 10100 => [1,2,3] => 1
[2,1,4,3,5] => [3,2] => 10100 => [1,2,3] => 1
[2,1,4,5,3] => [3,2] => 10100 => [1,2,3] => 1
[2,1,5,3,4] => [3,2] => 10100 => [1,2,3] => 1
[2,1,5,4,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[2,3,1,5,4] => [3,2] => 10100 => [1,2,3] => 1
[2,3,5,1,4] => [3,2] => 10100 => [1,2,3] => 1
[2,4,1,3,5] => [3,2] => 10100 => [1,2,3] => 1
[2,4,1,5,3] => [3,2] => 10100 => [1,2,3] => 1
[2,4,5,1,3] => [3,2] => 10100 => [1,2,3] => 1
[2,5,1,3,4] => [3,2] => 10100 => [1,2,3] => 1
[2,5,1,4,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[2,5,4,1,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,1,2,5,4] => [3,2] => 10100 => [1,2,3] => 1
[3,1,4,2,5] => [3,2] => 10100 => [1,2,3] => 1
[3,1,4,5,2] => [3,2] => 10100 => [1,2,3] => 1
[3,1,5,2,4] => [3,2] => 10100 => [1,2,3] => 1
[3,1,5,4,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,2,1,5,4] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,2,5,1,4] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,2,5,4,1] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,4,1,2,5] => [3,2] => 10100 => [1,2,3] => 1
[3,4,1,5,2] => [3,2] => 10100 => [1,2,3] => 1
[3,4,5,1,2] => [3,2] => 10100 => [1,2,3] => 1
[3,5,1,2,4] => [3,2] => 10100 => [1,2,3] => 1
[3,5,1,4,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,5,2,1,4] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,5,2,4,1] => [2,2,1] => 11010 => [1,1,2,2] => 1
[3,5,4,1,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,1,2,5,3] => [3,2] => 10100 => [1,2,3] => 1
[4,1,5,2,3] => [3,2] => 10100 => [1,2,3] => 1
[4,1,5,3,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,2,1,5,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,2,5,1,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,2,5,3,1] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,3,1,5,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,3,5,1,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,5,1,2,3] => [3,2] => 10100 => [1,2,3] => 1
[4,5,1,3,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,5,2,1,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,5,2,3,1] => [2,2,1] => 11010 => [1,1,2,2] => 1
[4,5,3,1,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[5,2,1,4,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[5,2,4,1,3] => [2,2,1] => 11010 => [1,1,2,2] => 1
[5,3,1,4,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[5,3,4,1,2] => [2,2,1] => 11010 => [1,1,2,2] => 1
[2,1,4,3,6,5] => [3,3] => 11000 => [1,1,4] => 1
[2,1,4,6,3,5] => [3,3] => 11000 => [1,1,4] => 1
[2,1,5,3,6,4] => [3,3] => 11000 => [1,1,4] => 1
[2,1,5,6,3,4] => [3,3] => 11000 => [1,1,4] => 1
[2,4,1,3,6,5] => [3,3] => 11000 => [1,1,4] => 1
[2,4,1,6,3,5] => [3,3] => 11000 => [1,1,4] => 1
[2,4,6,1,3,5] => [3,3] => 11000 => [1,1,4] => 1
[2,5,1,3,6,4] => [3,3] => 11000 => [1,1,4] => 1
[2,5,1,6,3,4] => [3,3] => 11000 => [1,1,4] => 1
[2,5,6,1,3,4] => [3,3] => 11000 => [1,1,4] => 1
[3,1,4,2,6,5] => [3,3] => 11000 => [1,1,4] => 1
[3,1,4,6,2,5] => [3,3] => 11000 => [1,1,4] => 1
[3,1,5,2,6,4] => [3,3] => 11000 => [1,1,4] => 1
[3,1,5,6,2,4] => [3,3] => 11000 => [1,1,4] => 1
[3,2,1,6,5,4] => [2,2,2] => 11100 => [1,1,1,3] => 1
[3,2,6,1,5,4] => [2,2,2] => 11100 => [1,1,1,3] => 1
[3,2,6,5,1,4] => [2,2,2] => 11100 => [1,1,1,3] => 1
[3,4,1,2,6,5] => [3,3] => 11000 => [1,1,4] => 1
>>> Load all 134 entries. <<<
[3,4,1,6,2,5] => [3,3] => 11000 => [1,1,4] => 1
[3,4,6,1,2,5] => [3,3] => 11000 => [1,1,4] => 1
[3,5,1,2,6,4] => [3,3] => 11000 => [1,1,4] => 1
[3,5,1,6,2,4] => [3,3] => 11000 => [1,1,4] => 1
[3,5,6,1,2,4] => [3,3] => 11000 => [1,1,4] => 1
[3,6,2,1,5,4] => [2,2,2] => 11100 => [1,1,1,3] => 1
[3,6,2,5,1,4] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,1,5,2,6,3] => [3,3] => 11000 => [1,1,4] => 1
[4,1,5,6,2,3] => [3,3] => 11000 => [1,1,4] => 1
[4,2,1,6,5,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,2,6,1,5,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,2,6,5,1,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,3,1,6,5,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,3,6,1,5,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,3,6,5,1,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,5,1,2,6,3] => [3,3] => 11000 => [1,1,4] => 1
[4,5,1,6,2,3] => [3,3] => 11000 => [1,1,4] => 1
[4,5,6,1,2,3] => [3,3] => 11000 => [1,1,4] => 1
[4,6,2,1,5,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,6,2,5,1,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,6,3,1,5,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[4,6,3,5,1,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,2,1,6,4,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,2,6,1,4,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,2,6,4,1,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,3,1,6,4,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,3,6,1,4,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,3,6,4,1,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,6,2,1,4,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,6,2,4,1,3] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,6,3,1,4,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[5,6,3,4,1,2] => [2,2,2] => 11100 => [1,1,1,3] => 1
[] => [] => => [1] => 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
Description
The dominant dimension of the corresponding Comp-Nakayama algebra.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
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 the shape of its corresponding insertion and recording tableau.
Map
to binary word
Description
Return the partition as binary word, by traversing its shape from the first row to the last row, down steps as 1 and left steps as 0.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.