- FindStat

Your data matches 20 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000790
(load all 3 compositions to match this statistic)

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
St000790: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

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

Description

The number of pairs of centered tunnels, one strictly containing the other, of a Dyck path. Apparently, the total number of these is given in [1]. The statistic counting all pairs of distinct tunnels is the area of a Dyck path [[St000012]].

Matching statistic: St001491

Mapping

Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00230: Integer partitions —parallelogram polyomino⟶ Dyck paths
Mp00093: Dyck paths —to binary word⟶ Binary words
St001491: Binary words ⟶ ℤResult quality: 19% ●values known / values provided: 19%●distinct values known / distinct values provided: 50%

Values

[-1,-2] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[2,-1] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,1] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,-3] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,2,-3] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,-2,3] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,-2,-3] => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? = 0
[1,3,-2] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,-3,2] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-1,3,-2] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,-3,2] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[2,-1,3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[2,-1,-3] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-2,1,3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,1,-3] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[2,3,-1] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[2,-3,1] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[-2,3,1] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[-2,-3,-1] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[3,1,-2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[3,-1,2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[-3,1,2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[-3,-1,-2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[3,2,-1] => [2]
 => [1,0,1,0]
 => 1010 => 0
[3,-2,-1] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-3,2,1] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-3,-2,1] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[1,-2,3,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[1,-2,-3,4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[1,-2,-3,-4] => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,2,-3,4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,2,-3,-4] => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,-2,3,-4] => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? = 0
[-1,-2,-3,4] => [1,1,1]
 => [1,1,0,1,0,0]
 => 110100 => ? = 0
[-1,-2,-3,-4] => [1,1,1,1]
 => [1,1,0,1,0,1,0,0]
 => 11010100 => ? = 1
[1,2,4,-3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,2,-4,3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,-2,4,-3] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[1,-2,-4,3] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,2,4,-3] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,2,-4,3] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,-2,4,3] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,-2,4,-3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 0
[-1,-2,-4,3] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 0
[-1,-2,-4,-3] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[1,3,-2,4] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,3,-2,-4] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[1,-3,2,4] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,-3,2,-4] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,3,2,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,3,-2,4] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,3,-2,-4] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 0
[-1,-3,2,4] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,-3,2,-4] => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => 10110100 => ? = 0
[-1,-3,-2,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[1,3,4,-2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[1,3,-4,2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[1,-3,4,2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[1,-3,-4,-2] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[-1,3,4,-2] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[-1,3,-4,2] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[-1,-3,4,2] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[-1,-3,-4,-2] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[1,4,2,-3] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[1,4,-2,3] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[1,-4,2,3] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[1,-4,-2,-3] => [3]
 => [1,0,1,0,1,0]
 => 101010 => ? = 0
[-1,4,2,-3] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[-1,4,-2,3] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[-1,-4,2,3] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[-1,-4,-2,-3] => [3,1]
 => [1,0,1,0,1,1,0,0]
 => 10101100 => ? = 0
[1,4,3,-2] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,4,-3,-2] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[1,-4,3,2] => [2]
 => [1,0,1,0]
 => 1010 => 0
[1,-4,-3,2] => [2,1]
 => [1,0,1,1,0,0]
 => 101100 => ? = 0
[-1,4,-3,2] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-1,-4,-3,-2] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[2,1,-3,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[2,-1,3,4] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,1,3,4] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,-1,-3,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[2,1,4,-3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[2,1,-4,3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[2,-1,4,3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[2,-1,-4,-3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,1,4,3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,1,-4,-3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,-1,4,-3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-2,-1,-4,3] => [2]
 => [1,0,1,0]
 => 1010 => 0
[3,2,-1,4] => [2]
 => [1,0,1,0]
 => 1010 => 0
[3,-2,1,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[-3,2,1,4] => [2]
 => [1,0,1,0]
 => 1010 => 0
[-3,-2,-1,-4] => [1,1]
 => [1,1,0,0]
 => 1100 => 1
[3,4,1,-2] => [2]
 => [1,0,1,0]
 => 1010 => 0
[3,4,-1,2] => [2]
 => [1,0,1,0]
 => 1010 => 0
[3,-4,1,2] => [2]
 => [1,0,1,0]
 => 1010 => 0
[3,-4,-1,-2] => [2]
 => [1,0,1,0]
 => 1010 => 0

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: St000512

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000512: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1
[2,-1] => []
 => ?
 => ?
 => ? = 0
[-2,1] => []
 => ?
 => ?
 => ? = 0
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0
[2,3,-1] => []
 => ?
 => ?
 => ? = 0
[2,-3,1] => []
 => ?
 => ?
 => ? = 0
[-2,3,1] => []
 => ?
 => ?
 => ? = 0
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0
[3,1,-2] => []
 => ?
 => ?
 => ? = 0
[3,-1,2] => []
 => ?
 => ?
 => ? = 0
[-3,1,2] => []
 => ?
 => ?
 => ? = 0
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 0

Description

The number of invariant subsets of size 3 when acting with a permutation of given cycle type.

Matching statistic: St000936

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000936: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1
[2,-1] => []
 => ?
 => ?
 => ? = 0
[-2,1] => []
 => ?
 => ?
 => ? = 0
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0
[2,3,-1] => []
 => ?
 => ?
 => ? = 0
[2,-3,1] => []
 => ?
 => ?
 => ? = 0
[-2,3,1] => []
 => ?
 => ?
 => ? = 0
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0
[3,1,-2] => []
 => ?
 => ?
 => ? = 0
[3,-1,2] => []
 => ?
 => ?
 => ? = 0
[-3,1,2] => []
 => ?
 => ?
 => ? = 0
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 0

Description

The number of even values of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation

$S^{(2,2)}$ are

$2$ on the conjugacy classes

$(4)$ and

$(2,2)$ ,

$0$ on the conjugacy classes

$(3,1)$ and

$(1,1,1,1)$ , and

$-1$ on the conjugace class

$(2,1,1)$ . Therefore, the statistic on the partition

$(2,2)$ is

$4$ . It is shown in [1] that the sum of the values of the statistic over all partitions of a given size is even.

Matching statistic: St000938

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000938: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1
[2,-1] => []
 => ?
 => ?
 => ? = 0
[-2,1] => []
 => ?
 => ?
 => ? = 0
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0
[2,3,-1] => []
 => ?
 => ?
 => ? = 0
[2,-3,1] => []
 => ?
 => ?
 => ? = 0
[-2,3,1] => []
 => ?
 => ?
 => ? = 0
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0
[3,1,-2] => []
 => ?
 => ?
 => ? = 0
[3,-1,2] => []
 => ?
 => ?
 => ? = 0
[-3,1,2] => []
 => ?
 => ?
 => ? = 0
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 0

Description

The number of zeros of the symmetric group character corresponding to the partition. For example, the character values of the irreducible representation

$S^{(2,2)}$ are

$2$ on the conjugacy classes

$(4)$ and

$(2,2)$ ,

$0$ on the conjugacy classes

$(3,1)$ and

$(1,1,1,1)$ , and

$-1$ on the conjugacy class

$(2,1,1)$ . Therefore, the statistic on the partition

$(2,2)$ is

$2$ .

Matching statistic: St000940

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000940: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1
[2,-1] => []
 => ?
 => ?
 => ? = 0
[-2,1] => []
 => ?
 => ?
 => ? = 0
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0
[2,3,-1] => []
 => ?
 => ?
 => ? = 0
[2,-3,1] => []
 => ?
 => ?
 => ? = 0
[-2,3,1] => []
 => ?
 => ?
 => ? = 0
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0
[3,1,-2] => []
 => ?
 => ?
 => ? = 0
[3,-1,2] => []
 => ?
 => ?
 => ? = 0
[-3,1,2] => []
 => ?
 => ?
 => ? = 0
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 0

Description

The number of characters of the symmetric group whose value on the partition is zero. The maximal value for any given size is recorded in [2].

Matching statistic: St000941

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000941: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1
[2,-1] => []
 => ?
 => ?
 => ? = 0
[-2,1] => []
 => ?
 => ?
 => ? = 0
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0
[2,3,-1] => []
 => ?
 => ?
 => ? = 0
[2,-3,1] => []
 => ?
 => ?
 => ? = 0
[-2,3,1] => []
 => ?
 => ?
 => ? = 0
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0
[3,1,-2] => []
 => ?
 => ?
 => ? = 0
[3,-1,2] => []
 => ?
 => ?
 => ? = 0
[-3,1,2] => []
 => ?
 => ?
 => ? = 0
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 0

Description

The number of characters of the symmetric group whose value on the partition is even.

Matching statistic: St001124

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001124: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1
[2,-1] => []
 => ?
 => ?
 => ? = 0
[-2,1] => []
 => ?
 => ?
 => ? = 0
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0
[2,3,-1] => []
 => ?
 => ?
 => ? = 0
[2,-3,1] => []
 => ?
 => ?
 => ? = 0
[-2,3,1] => []
 => ?
 => ?
 => ? = 0
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0
[3,1,-2] => []
 => ?
 => ?
 => ? = 0
[3,-1,2] => []
 => ?
 => ?
 => ? = 0
[-3,1,2] => []
 => ?
 => ?
 => ? = 0
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 0
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 0

Description

The multiplicity of the standard representation in the Kronecker square corresponding to a partition. The Kronecker coefficient is the multiplicity

$g_{\mu,\nu}^\lambda$ of the Specht module

$S^\lambda$ in

$S^\mu\otimes S^\nu$ :

$S^\mu\otimes S^\nu = \bigoplus_\lambda g_{\mu,\nu}^\lambda S^\lambda$ This statistic records the Kronecker coefficient

$g_{\lambda,\lambda}^{(n-1)1}$ , for

$\lambda\vdash n > 1$ . For

$n\leq1$ the statistic is undefined. It follows from [3, Prop.4.1] (or, slightly easier from [3, Thm.4.2]) that this is one less than [[St000159]], the number of distinct parts of the partition.

Matching statistic: St000284

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000284: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1 + 1
[2,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,1] => []
 => ?
 => ?
 => ? = 0 + 1
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1 + 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1 + 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1 + 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0 + 1
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0 + 1
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0 + 1
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[2,3,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[2,-3,1] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,3,1] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[3,1,-2] => []
 => ?
 => ?
 => ? = 0 + 1
[3,-1,2] => []
 => ?
 => ?
 => ? = 0 + 1
[-3,1,2] => []
 => ?
 => ?
 => ? = 0 + 1
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0 + 1
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0 + 1
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0 + 1
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0 + 1
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1 + 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0 + 1
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0 + 1
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0 + 1
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1 + 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0 + 1
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1 + 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0 + 1
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1 = 0 + 1

Description

The Plancherel distribution on integer partitions. This is defined as the distribution induced by the RSK shape of the uniform distribution on permutations. In other words, this is the size of the preimage of the map 'Robinson-Schensted tableau shape' from permutations to integer partitions. Equivalently, this is given by the square of the number of standard Young tableaux of the given shape.

Matching statistic: St000510

Mapping

Mp00166: Signed permutations —even cycle type⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St000510: Integer partitions ⟶ ℤResult quality: 1% ●values known / values provided: 1%●distinct values known / distinct values provided: 25%

Values

[-1,-2] => []
 => ?
 => ?
 => ? = 1 + 1
[2,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,1] => []
 => ?
 => ?
 => ? = 0 + 1
[1,-2,-3] => [1]
 => []
 => ?
 => ? = 1 + 1
[-1,2,-3] => [1]
 => []
 => ?
 => ? = 1 + 1
[-1,-2,3] => [1]
 => []
 => ?
 => ? = 1 + 1
[-1,-2,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[1,3,-2] => [1]
 => []
 => ?
 => ? = 0 + 1
[1,-3,2] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,3,-2] => []
 => ?
 => ?
 => ? = 0 + 1
[-1,-3,2] => []
 => ?
 => ?
 => ? = 0 + 1
[2,-1,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[2,-1,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,1,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-2,1,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[2,3,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[2,-3,1] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,3,1] => []
 => ?
 => ?
 => ? = 0 + 1
[-2,-3,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[3,1,-2] => []
 => ?
 => ?
 => ? = 0 + 1
[3,-1,2] => []
 => ?
 => ?
 => ? = 0 + 1
[-3,1,2] => []
 => ?
 => ?
 => ? = 0 + 1
[-3,-1,-2] => []
 => ?
 => ?
 => ? = 0 + 1
[3,2,-1] => [1]
 => []
 => ?
 => ? = 0 + 1
[3,-2,-1] => []
 => ?
 => ?
 => ? = 0 + 1
[-3,2,1] => [1]
 => []
 => ?
 => ? = 0 + 1
[-3,-2,1] => []
 => ?
 => ?
 => ? = 0 + 1
[1,2,-3,-4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[1,-2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[1,-2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[1,-2,-3,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,2,3,-4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[-1,2,-3,4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[-1,2,-3,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,3,4] => [1,1]
 => [1]
 => []
 => ? = 1 + 1
[-1,-2,3,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,-3,4] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,-3,-4] => []
 => ?
 => ?
 => ? = 1 + 1
[1,2,4,-3] => [1,1]
 => [1]
 => []
 => ? = 0 + 1
[1,2,-4,3] => [1,1]
 => [1]
 => []
 => ? = 0 + 1
[1,-2,4,-3] => [1]
 => []
 => ?
 => ? = 0 + 1
[1,-2,-4,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,2,4,-3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,2,-4,3] => [1]
 => []
 => ?
 => ? = 0 + 1
[-1,-2,4,3] => [2]
 => []
 => ?
 => ? = 1 + 1
[-1,-2,4,-3] => []
 => ?
 => ?
 => ? = 0 + 1
[-1,-2,-4,3] => []
 => ?
 => ?
 => ? = 0 + 1
[-1,-2,-4,-3] => [2]
 => []
 => ?
 => ? = 1 + 1
[1,3,-2,4] => [1,1]
 => [1]
 => []
 => ? = 0 + 1
[1,3,-2,-4] => [1]
 => []
 => ?
 => ? = 0 + 1
[1,2,3,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,6,5,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,6,4,5,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,3,4,5,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,3,4,5,-1] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[-2,1,3,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,7,1,4,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,7,3,1,5,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,7,3,4,1,6,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,7,3,4,5,1,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,1,3,4,5,6,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,4,7,2,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,5,7,4,2,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,7,4,5,2,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,2,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[4,2,7,1,5,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,2,7,4,1,6,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,7,4,5,1,-3] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,1,4,5,6,-3] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,5,7,3,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,6,7,5,3,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,7,3,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,5,3,7,2,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,3,7,5,2,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,3,2,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,2,3,7,1,6,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,3,7,5,1,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,3,1,5,6,-4] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,6,7,4,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,7,4,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,6,4,7,3,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,7,4,3,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,3,4,7,2,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,3,4,2,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[6,2,3,4,7,1,-5] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,3,4,1,6,-5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,4,7,5,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,7,5,4,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,7,4,5,3,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,7,3,4,5,2,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[7,2,3,4,5,1,-6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,4,3,6,5,8,7,-2] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,-3,2,4,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,-4,3,5,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,-5,4,6] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,2,3,4,-6,5] => [1,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,1,6,5,8,7,-4] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[3,2,5,4,1,8,7,-6] => [3,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[1,6,5,4,3,8,7,-2] => [2,1,1,1]
 => [1,1,1]
 => [1,1]
 => 1 = 0 + 1
[5,4,3,2,1,8,7,-6] => [2,2,1,1]
 => [2,1,1]
 => [1,1]
 => 1 = 0 + 1

Description

The number of invariant oriented cycles when acting with a permutation of given cycle type.

The following 10 statistics, ordered by result quality, also match your data. Click on any of them to see the details.

St000681The Grundy value of Chomp on Ferrers diagrams. 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. St001123The multiplicity of the dual of the standard representation in the Kronecker square corresponding to a partition. St001128The exponens consonantiae of a partition. St000514The number of invariant simple graphs when acting with a permutation of given cycle type. St000515The number of invariant set partitions when acting with a permutation of given cycle type. St001604The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons. St001603The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.