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
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
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 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.