- FindStat

Your data matches 201 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001603
(load all 2 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00313: Integer partitions —Glaisher-Franklin inverse⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001603: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[2,3,4,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[2,3,-4,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[2,-3,4,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[2,-3,-4,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,3,4,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,3,-4,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,-3,4,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,-3,-4,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[2,4,1,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[2,4,-1,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[2,-4,1,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[2,-4,-1,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,4,1,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,4,-1,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,-4,1,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-2,-4,-1,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,1,4,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,1,-4,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,-1,4,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,-1,-4,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,1,4,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,1,-4,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,-1,4,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,-1,-4,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,4,2,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,4,-2,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,-4,2,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[3,-4,-2,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,4,2,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,4,-2,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,-4,2,-1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-3,-4,-2,1] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,1,2,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,1,-2,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,-1,2,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,-1,-2,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,1,2,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,1,-2,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,-1,2,-3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,-1,-2,3] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,3,1,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,3,-1,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,-3,1,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[4,-3,-1,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,3,1,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,3,-1,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,-3,1,-2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-4,-3,-1,2] => [4]
 => [1,1,1,1]
 => [1,1,1]
 => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [2,2,1]
 => [2,1]
 => 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [2,1,1,1]
 => [1,1,1]
 => 1

Description

The number of colourings of a polygon such that the multiplicities of a colour are given by a partition. Two colourings are considered equal, if they are obtained by an action of the dihedral group. This statistic is only defined for partitions of size at least 3, to avoid ambiguity.

Matching statistic: St001195
(load all 3 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[2,3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[2,-3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[2,-3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,-3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,-3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[2,4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[2,4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[2,-4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[2,-4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,-4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-2,-4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,-1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,-1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,-1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,-1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,-4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[3,-4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,-4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-3,-4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,-1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,-1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,-1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,-1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,-3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[4,-3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,-3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-4,-3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[1,3,4,5,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[1,3,4,-5,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1
[-1,3,4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => ? = 3

Description

The global dimension of the algebra

$A/AfA$ of the corresponding Nakayama algebra

$A$ with minimal left faithful projective-injective module

$Af$ .

Matching statistic: St001207
(load all 88 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4] => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[1,3,4,5,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[1,3,4,-5,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-1,3,4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3

Description

The Lowey length of the algebra

$A/T$ when

$T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra of

$K[x]/(x^n)$ .

Matching statistic: St001208
(load all 3 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001208: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[1,3,4,5,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[1,3,4,-5,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-1,3,4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3

Description

The number of connected components of the quiver of

$A/T$ when

$T$ is the 1-tilting module corresponding to the permutation in the Auslander algebra

$A$ of

$K[x]/(x^n)$ .

Matching statistic: St001236

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
Mp00178: Binary words —to composition⟶ Integer compositions
St001236: Integer compositions ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => 10000 => [1,5] => 1
[2,3,-4,1] => [4]
 => 10000 => [1,5] => 1
[2,-3,4,1] => [4]
 => 10000 => [1,5] => 1
[2,-3,-4,-1] => [4]
 => 10000 => [1,5] => 1
[-2,3,4,1] => [4]
 => 10000 => [1,5] => 1
[-2,3,-4,-1] => [4]
 => 10000 => [1,5] => 1
[-2,-3,4,-1] => [4]
 => 10000 => [1,5] => 1
[-2,-3,-4,1] => [4]
 => 10000 => [1,5] => 1
[2,4,1,-3] => [4]
 => 10000 => [1,5] => 1
[2,4,-1,3] => [4]
 => 10000 => [1,5] => 1
[2,-4,1,3] => [4]
 => 10000 => [1,5] => 1
[2,-4,-1,-3] => [4]
 => 10000 => [1,5] => 1
[-2,4,1,3] => [4]
 => 10000 => [1,5] => 1
[-2,4,-1,-3] => [4]
 => 10000 => [1,5] => 1
[-2,-4,1,-3] => [4]
 => 10000 => [1,5] => 1
[-2,-4,-1,3] => [4]
 => 10000 => [1,5] => 1
[3,1,4,-2] => [4]
 => 10000 => [1,5] => 1
[3,1,-4,2] => [4]
 => 10000 => [1,5] => 1
[3,-1,4,2] => [4]
 => 10000 => [1,5] => 1
[3,-1,-4,-2] => [4]
 => 10000 => [1,5] => 1
[-3,1,4,2] => [4]
 => 10000 => [1,5] => 1
[-3,1,-4,-2] => [4]
 => 10000 => [1,5] => 1
[-3,-1,4,-2] => [4]
 => 10000 => [1,5] => 1
[-3,-1,-4,2] => [4]
 => 10000 => [1,5] => 1
[3,4,2,-1] => [4]
 => 10000 => [1,5] => 1
[3,4,-2,1] => [4]
 => 10000 => [1,5] => 1
[3,-4,2,1] => [4]
 => 10000 => [1,5] => 1
[3,-4,-2,-1] => [4]
 => 10000 => [1,5] => 1
[-3,4,2,1] => [4]
 => 10000 => [1,5] => 1
[-3,4,-2,-1] => [4]
 => 10000 => [1,5] => 1
[-3,-4,2,-1] => [4]
 => 10000 => [1,5] => 1
[-3,-4,-2,1] => [4]
 => 10000 => [1,5] => 1
[4,1,2,-3] => [4]
 => 10000 => [1,5] => 1
[4,1,-2,3] => [4]
 => 10000 => [1,5] => 1
[4,-1,2,3] => [4]
 => 10000 => [1,5] => 1
[4,-1,-2,-3] => [4]
 => 10000 => [1,5] => 1
[-4,1,2,3] => [4]
 => 10000 => [1,5] => 1
[-4,1,-2,-3] => [4]
 => 10000 => [1,5] => 1
[-4,-1,2,-3] => [4]
 => 10000 => [1,5] => 1
[-4,-1,-2,3] => [4]
 => 10000 => [1,5] => 1
[4,3,1,-2] => [4]
 => 10000 => [1,5] => 1
[4,3,-1,2] => [4]
 => 10000 => [1,5] => 1
[4,-3,1,2] => [4]
 => 10000 => [1,5] => 1
[4,-3,-1,-2] => [4]
 => 10000 => [1,5] => 1
[-4,3,1,2] => [4]
 => 10000 => [1,5] => 1
[-4,3,-1,-2] => [4]
 => 10000 => [1,5] => 1
[-4,-3,1,-2] => [4]
 => 10000 => [1,5] => 1
[-4,-3,-1,2] => [4]
 => 10000 => [1,5] => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => 111110 => [1,1,1,1,1,2] => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[1,3,4,5,-2] => [4]
 => 10000 => [1,5] => 1
[1,3,4,-5,2] => [4]
 => 10000 => [1,5] => 1
[-1,3,4,5,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,3,4,-5,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,3,-4,5,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,4,5,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,3,5,2,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,3,5,-2,4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,3,-5,2,4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,5,2,4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,2,5,-3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,2,-5,3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,-2,5,3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,2,5,3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => 101110 => [1,2,1,1,2] => ? = 1
[-1,4,5,3,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,5,-3,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,-5,3,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,5,3,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,5,2,3,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,5,2,-3,4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,5,-2,3,4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-5,2,3,4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => 100010 => [1,4,2] => ? = 3

Description

The dominant dimension of the corresponding Comp-Nakayama algebra.

Matching statistic: St001436
(load all 3 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001436: Binary words ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[2,3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[2,-3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[2,-3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,-3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,-3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[2,4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[2,4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[2,-4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[2,-4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,-4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-2,-4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,-1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,-1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,-1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,-1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,-4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[3,-4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,-4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-3,-4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,-1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,-1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,-1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,-1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,-3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[4,-3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,-3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-4,-3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => 1101010100 => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[1,3,4,5,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[1,3,4,-5,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => 10101010 => 1
[-1,3,4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => 1011010100 => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => 1010101100 => ? = 3

Description

The index of a given binary word in the lex-order among all its cyclic shifts.

Matching statistic: St001491
(load all 4 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00321: Integer partitions —2-conjugate⟶ Integer partitions
Mp00095: Integer partitions —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [2,2]
 => 1100 => 1
[2,3,-4,1] => [4]
 => [2,2]
 => 1100 => 1
[2,-3,4,1] => [4]
 => [2,2]
 => 1100 => 1
[2,-3,-4,-1] => [4]
 => [2,2]
 => 1100 => 1
[-2,3,4,1] => [4]
 => [2,2]
 => 1100 => 1
[-2,3,-4,-1] => [4]
 => [2,2]
 => 1100 => 1
[-2,-3,4,-1] => [4]
 => [2,2]
 => 1100 => 1
[-2,-3,-4,1] => [4]
 => [2,2]
 => 1100 => 1
[2,4,1,-3] => [4]
 => [2,2]
 => 1100 => 1
[2,4,-1,3] => [4]
 => [2,2]
 => 1100 => 1
[2,-4,1,3] => [4]
 => [2,2]
 => 1100 => 1
[2,-4,-1,-3] => [4]
 => [2,2]
 => 1100 => 1
[-2,4,1,3] => [4]
 => [2,2]
 => 1100 => 1
[-2,4,-1,-3] => [4]
 => [2,2]
 => 1100 => 1
[-2,-4,1,-3] => [4]
 => [2,2]
 => 1100 => 1
[-2,-4,-1,3] => [4]
 => [2,2]
 => 1100 => 1
[3,1,4,-2] => [4]
 => [2,2]
 => 1100 => 1
[3,1,-4,2] => [4]
 => [2,2]
 => 1100 => 1
[3,-1,4,2] => [4]
 => [2,2]
 => 1100 => 1
[3,-1,-4,-2] => [4]
 => [2,2]
 => 1100 => 1
[-3,1,4,2] => [4]
 => [2,2]
 => 1100 => 1
[-3,1,-4,-2] => [4]
 => [2,2]
 => 1100 => 1
[-3,-1,4,-2] => [4]
 => [2,2]
 => 1100 => 1
[-3,-1,-4,2] => [4]
 => [2,2]
 => 1100 => 1
[3,4,2,-1] => [4]
 => [2,2]
 => 1100 => 1
[3,4,-2,1] => [4]
 => [2,2]
 => 1100 => 1
[3,-4,2,1] => [4]
 => [2,2]
 => 1100 => 1
[3,-4,-2,-1] => [4]
 => [2,2]
 => 1100 => 1
[-3,4,2,1] => [4]
 => [2,2]
 => 1100 => 1
[-3,4,-2,-1] => [4]
 => [2,2]
 => 1100 => 1
[-3,-4,2,-1] => [4]
 => [2,2]
 => 1100 => 1
[-3,-4,-2,1] => [4]
 => [2,2]
 => 1100 => 1
[4,1,2,-3] => [4]
 => [2,2]
 => 1100 => 1
[4,1,-2,3] => [4]
 => [2,2]
 => 1100 => 1
[4,-1,2,3] => [4]
 => [2,2]
 => 1100 => 1
[4,-1,-2,-3] => [4]
 => [2,2]
 => 1100 => 1
[-4,1,2,3] => [4]
 => [2,2]
 => 1100 => 1
[-4,1,-2,-3] => [4]
 => [2,2]
 => 1100 => 1
[-4,-1,2,-3] => [4]
 => [2,2]
 => 1100 => 1
[-4,-1,-2,3] => [4]
 => [2,2]
 => 1100 => 1
[4,3,1,-2] => [4]
 => [2,2]
 => 1100 => 1
[4,3,-1,2] => [4]
 => [2,2]
 => 1100 => 1
[4,-3,1,2] => [4]
 => [2,2]
 => 1100 => 1
[4,-3,-1,-2] => [4]
 => [2,2]
 => 1100 => 1
[-4,3,1,2] => [4]
 => [2,2]
 => 1100 => 1
[-4,3,-1,-2] => [4]
 => [2,2]
 => 1100 => 1
[-4,-3,1,-2] => [4]
 => [2,2]
 => 1100 => 1
[-4,-3,-1,2] => [4]
 => [2,2]
 => 1100 => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,1,1,1]
 => 111110 => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[1,3,4,5,-2] => [4]
 => [2,2]
 => 1100 => 1
[1,3,4,-5,2] => [4]
 => [2,2]
 => 1100 => 1
[-1,3,4,5,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [3,1,1]
 => 100110 => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [3,2]
 => 10100 => ? = 3

Description

The number of indecomposable projective-injective modules in the algebra corresponding to a subset. Let

$A_n=K[x]/(x^n)$ . We associate to a nonempty subset S of an (n-1)-set the module

$M_S$ , which is the direct sum of

$A_n$ -modules with indecomposable non-projective direct summands of dimension

$i$ when

$i$ is in

$S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of

$M_S$ . We decode the subset as a binary word so that for example the subset

$S=\{1,3 \}$ of

$\{1,2,3 \}$ is decoded as 101.

Matching statistic: St001520
(load all 2 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001520: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[1,3,4,5,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[1,3,4,-5,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-1,3,4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3

Description

The number of strict 3-descents. A '''strict 3-descent''' of a permutation

$\pi$ of

$\{1,2, \dots ,n \}$ is a pair

$(i,i+3)$ with

$i+3 \leq n$ and

$\pi(i) > \pi(i+3)$ .

Matching statistic: St001569
(load all 2 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001569: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[2,-4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-2,-4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[3,-4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-3,-4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[4,-3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-4,-3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [5,6,1,2,3,4] => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[1,3,4,5,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[1,3,4,-5,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => 1
[-1,3,4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [5,1,2,3,6,4] => ? = 3

Description

The maximal modular displacement of a permutation. This is

$\max_{1\leq i \leq n} \left(\min(\pi(i)-i\pmod n, i-\pi(i)\pmod n)\right)$ for a permutation

$\pi$ of

$\{1,\dots,n\}$ .

Matching statistic: St001582
(load all 20 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 38%●distinct values known / distinct values provided: 17%

Values

[2,3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,3,4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,3,-4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-3,4,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-3,-4,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[2,-4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,4,1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,4,-1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-4,1,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-2,-4,-1,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,1,4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,1,-4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-1,4,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-1,-4,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[3,-4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,4,2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,4,-2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-4,2,-1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-3,-4,-2,1] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,1,2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,1,-2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-1,2,-3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-1,-2,3] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[4,-3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,3,1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,3,-1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-3,1,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-4,-3,-1,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-1,-2,-3,-4,-5] => [1,1,1,1,1]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,3,2,5,4] => ? = 1
[-1,-2,-3,5,-4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,-3,-5,4] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,4,-3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,-4,3,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,5,-4,-3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-2,-5,-4,3] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,3,-2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-3,2,-4,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[1,3,4,5,-2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[1,3,4,-5,2] => [4]
 => [1,0,1,0,1,0,1,0]
 => [2,1,4,3] => 1
[-1,3,4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,4,5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,4,-5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-4,5,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-4,-5,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,3,-5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,5,2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,5,-2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-5,2,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-3,-5,-2,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,2,5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,2,-5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-2,5,-3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-2,-5,3] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-3,-2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,-4,-3,2,-5] => [2,1,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [2,3,1,5,4] => ? = 1
[-1,4,5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,4,-5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,5,3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,5,-3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-5,3,-2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-4,-5,-3,2] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,2,-3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,-2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,5,-2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-5,2,3,4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-5,2,-3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3
[-1,-5,-2,3,-4] => [4,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [2,4,1,3,5] => ? = 3

Description

The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.

The following 191 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St001686The order of promotion on a Gelfand-Tsetlin pattern. St001885The number of binary words with the same proper border set. St000508Eigenvalues of the random-to-random operator acting on a simple module. St000543The size of the conjugacy class of a binary word. St000626The minimal period of a binary word. St000682The Grundy value of Welter's game on a binary word. St000689The maximal n such that the minimal generator-cogenerator module in the LNakayama algebra of a Dyck path is n-rigid. St000693The modular (standard) major index of a standard tableau. St000753The Grundy value for the game of Kayles on a binary word. St001001The number of indecomposable modules with projective and injective dimension equal to the global dimension of the Nakayama algebra corresponding to the Dyck path. St001171The vector space dimension of

$Ext_A^1(I_o,A)$ when

$I_o$ is the tilting module corresponding to the permutation

$o$ in the Auslander algebra

$A$ of

$K[x]/(x^n)$ . St001235The global dimension of the corresponding Comp-Nakayama algebra. St001371The length of the longest Yamanouchi prefix of a binary word. St001413Half the length of the longest even length palindromic prefix of a binary word. St001423The number of distinct cubes in a binary word. St001485The modular major index of a binary word. St001524The degree of symmetry of a binary word. St001556The number of inversions of the third entry of a permutation. St001557The number of inversions of the second entry of a permutation. St001583The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order. St001730The number of times the path corresponding to a binary word crosses the base line. St001803The maximal overlap of the cylindrical tableau associated with a tableau. St001804The minimal height of the rectangular inner shape in a cylindrical tableau associated to a tableau. St001811The Castelnuovo-Mumford regularity of a permutation. St001856The number of edges in the reduced word graph of a permutation. St001948The number of augmented double ascents of a permutation. St001960The number of descents of a permutation minus one if its first entry is not one. St001000Number of indecomposable modules with projective dimension equal to the global dimension in the Nakayama algebra corresponding to the Dyck path. St001314The number of tilting modules of arbitrary projective dimension that have no simple modules as a direct summand in the corresponding Nakayama algebra. St001414Half the length of the longest odd length palindromic prefix of a binary word. St001424The number of distinct squares in a binary word. St001514The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule. St001526The Loewy length of the Auslander-Reiten translate of the regular module as a bimodule of the Nakayama algebra corresponding to the Dyck path. St001712The number of natural descents of a standard Young tableau. St000186The sum of the first row in a Gelfand-Tsetlin pattern. St000735The last entry on the main diagonal of a standard tableau. St000744The length of the path to the largest entry in a standard Young tableau. St001002Number of indecomposable modules with projective and injective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001200The number of simple modules in

$eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra

$A$ with minimal faithful projective-injective module

$eA$ . St001355Number of non-empty prefixes of a binary word that contain equally many 0's and 1's. St001406The number of nonzero entries in a Gelfand Tsetlin pattern. St001420Half the length of a longest factor which is its own reverse-complement of a binary word. St001421Half the length of a longest factor which is its own reverse-complement and begins with a one of a binary word. St001431Half of the Loewy length minus one of a modified stable Auslander algebra of the Nakayama algebra corresponding to the Dyck path. St001462The number of factors of a standard tableaux under concatenation. St001515The vector space dimension of the socle of the first syzygy module of the regular module (as a bimodule). St001553The number of indecomposable summands of the square of the Jacobson radical as a bimodule in the Nakayama algebra corresponding to the Dyck path. St001684The reduced word complexity of a permutation. St001884The number of borders of a binary word. St000044The number of vertices of the unicellular map given by a perfect matching. St000393The number of strictly increasing runs in a binary word. St000950Number of tilting modules of the corresponding LNakayama algebra, where a tilting module is a generalised tilting module of projective dimension 1. St001267The length of the Lyndon factorization of the binary word. St001404The number of distinct entries in a Gelfand Tsetlin pattern. St000017The number of inversions of a standard tableau. St000295The length of the border of a binary word. St000519The largest length of a factor maximising the subword complexity. St000691The number of changes of a binary word. St000922The minimal number such that all substrings of this length are unique. St001415The length of the longest palindromic prefix of a binary word. St001416The length of a longest palindromic factor of a binary word. St001417The length of a longest palindromic subword of a binary word. St001419The length of the longest palindromic factor beginning with a one of a binary word. St001721The degree of a binary word. St000983The length of the longest alternating subword. St001003The number of indecomposable modules with projective dimension at most 1 in the Nakayama algebra corresponding to the Dyck path. St001838The number of nonempty primitive factors of a binary word. St001695The natural comajor index of a standard Young tableau. St001698The comajor index of a standard tableau minus the weighted size of its shape. St001699The major index of a standard tableau minus the weighted size of its shape. St000348The non-inversion sum of a binary word. St000826The stopping time of the decimal representation of the binary word for the 3x+1 problem. St001313The number of Dyck paths above the lattice path given by a binary word. St000294The number of distinct factors of a binary word. St000391The sum of the positions of the ones in a binary word. St001697The shifted natural comajor index of a standard Young tableau. St001930The weak major index of a binary word. St000016The number of attacking pairs of a standard tableau. St000545The number of parabolic double cosets with minimal element being the given permutation. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of

$K[x]/(x^n)$ . St000631The number of distinct palindromic decompositions of a binary word. St000949Gives the number of generalised tilting modules of the corresponding LNakayama algebra. St000033The number of permutations greater than or equal to the given permutation in (strong) Bruhat order. St000958The number of Bruhat factorizations of a permutation. St000347The inversion sum of a binary word. St000847The number of standard Young tableaux whose descent set is the binary word. St001365The number of lattice paths of the same length weakly above the path given by a binary word. St000518The number of distinct subsequences in a binary word. St001916The number of transient elements in the orbit of Bulgarian solitaire corresponding to a necklace. St001915The size of the component corresponding to a necklace in Bulgarian solitaire. St001560The product of the cardinalities of the lower order ideal and upper order ideal generated by a permutation in weak order. St001243The sum of coefficients in the Schur basis of certain LLT polynomials associated with a Dyck path. St000289The decimal representation of a binary word. St000827The decimal representation of a binary word with a leading 1. St001242The toal dimension of certain Sn modules determined by LLT polynomials associated with a Dyck path. St000618The number of self-evacuating tableaux of given shape. St000781The number of proper colouring schemes of a Ferrers diagram. St001432The order dimension of the partition. St001599The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on rooted trees. St001780The order of promotion on the set of standard tableaux of given shape. St001899The total number of irreducible representations contained in the higher Lie character for an integer partition. St001900The number of distinct irreducible representations contained in the higher Lie character for an integer partition. St001901The largest multiplicity of an irreducible representation contained in the higher Lie character for an integer partition. St001908The number of semistandard tableaux of distinct weight whose maximal entry is the length of the partition. St001924The number of cells in an integer partition whose arm and leg length coincide. St001934The number of monotone factorisations of genus zero of a permutation of given cycle type. St000175Degree of the polynomial counting the number of semistandard Young tableaux when stretching the shape. St000205Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and partition weight. St000206Number of non-integral Gelfand-Tsetlin polytopes with prescribed top row and integer composition weight. St000225Difference between largest and smallest parts in a partition. St000749The smallest integer d such that the restriction of the representation corresponding to a partition of n to the symmetric group on n-d letters has a constituent of odd degree. St000944The 3-degree of an integer partition. St001175The size of a partition minus the hook length of the base cell. St001178Twelve times the variance of the major index among all standard Young tableaux of a partition. St001586The number of odd parts smaller than the largest even part in an integer partition. St000908The length of the shortest maximal antichain in a poset. St000914The sum of the values of the Möbius function of a poset. St001301The first Betti number of the order complex associated with the poset. St001634The trace of the Coxeter matrix of the incidence algebra of a poset. St001864The number of excedances of a signed permutation. St001867The number of alignments of type EN of a signed permutation. St001889The size of the connectivity set of a signed permutation. St001532The leading coefficient of the Poincare polynomial of the poset cone. St001396Number of triples of incomparable elements in a finite poset. St001472The permanent of the Coxeter matrix of the poset. St000680The Grundy value for Hackendot on posets. St000912The number of maximal antichains in a poset. St001858The number of covering elements of a signed permutation in absolute order. St000188The area of the Dyck path corresponding to a parking function and the total displacement of a parking function. St000195The number of secondary dinversion pairs of the dyck path corresponding to a parking function. St000943The number of spots the most unlucky car had to go further in a parking function. St001903The number of fixed points of a parking function. St000135The number of lucky cars of the parking function. St001927Sparre Andersen's number of positives of a signed permutation. St000540The sum of the entries of a parking function minus its length. St000165The sum of the entries of a parking function. St000942The number of critical left to right maxima of the parking functions. St001490The number of connected components of a skew partition. St001768The number of reduced words of a signed permutation. St001860The number of factors of the Stanley symmetric function associated with a signed permutation. St001904The length of the initial strictly increasing segment of a parking function. St001738The minimal order of a graph which is not an induced subgraph of the given graph. St001926Sparre Andersen's position of the maximum of a signed permutation. St001434The number of negative sum pairs of a signed permutation. St001854The size of the left Kazhdan-Lusztig cell, St000284The Plancherel distribution on integer partitions. St000698The number of 2-rim hooks removed from an integer partition to obtain its associated 2-core. St000704The number of semistandard tableaux on a given integer partition with minimal maximal entry. St000901The cube of the number of standard Young tableaux with shape given by the partition. St001128The exponens consonantiae of a partition. St000936The number of even values of the symmetric group character corresponding to the partition. St000938The number of zeros of the symmetric group character corresponding to the partition. St000940The number of characters of the symmetric group whose value on the partition is zero. St001124The multiplicity of the standard representation in the Kronecker square corresponding to a partition. St000633The size of the automorphism group of a poset. St001399The distinguishing number of a poset. St000850The number of 1/2-balanced pairs in a poset. St001343The dimension of the reduced incidence algebra of a poset. St000180The number of chains of a poset. St000620The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is odd. St000668The least common multiple of the parts of the partition. St000707The product of the factorials of the parts. St000708The product of the parts of an integer partition. St000770The major index of an integer partition when read from bottom to top. St000815The number of semistandard Young tableaux of partition weight of given shape. St000929The constant term of the character polynomial of an integer partition. St000933The number of multipartitions of sizes given by an integer partition. St000478Another weight of a partition according to Alladi. St000566The number of ways to select a row of a Ferrers shape and two cells in this row. St000621The number of standard tableaux of shape equal to the given partition such that the minimal cyclic descent is even. St000934The 2-degree of an integer partition. St001568The smallest positive integer that does not appear twice in the partition. St000716The dimension of the irreducible representation of Sp(6) labelled by an integer partition. St000477The weight of a partition according to Alladi. St000713The dimension of the irreducible representation of Sp(4) labelled by an integer partition. St000714The number of semistandard Young tableau of given shape, with entries at most 2. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St000706The product of the factorials of the multiplicities of an integer partition. St000813The number of zero-one matrices with weakly decreasing column sums and row sums given by the partition. St000928The sum of the coefficients of the character polynomial of an integer partition. St000993The multiplicity of the largest part of an integer partition. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001605The number of colourings of a cycle such that the multiplicities of colours are given by a partition. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St000567The sum of the products of all pairs of parts. St001097The coefficient of the monomial symmetric function indexed by the partition in the formal group law for linear orders. St001098The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for vertex labelled trees. St001099The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled binary trees. St001100The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for leaf labelled trees. St001101The coefficient times the product of the factorials of the parts of the monomial symmetric function indexed by the partition in the formal group law for increasing trees. St000997The even-odd crank of an integer partition.