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Matching statistic: St000941
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00308: Integer partitions —Bulgarian solitaire⟶ Integer partitions
St000941: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00308: Integer partitions —Bulgarian solitaire⟶ Integer partitions
St000941: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-1,-2] => [1,1]
=> [2]
=> 0
[2,-1] => [2]
=> [1,1]
=> 0
[-2,1] => [2]
=> [1,1]
=> 0
[1,-2,-3] => [1,1]
=> [2]
=> 0
[-1,2,-3] => [1,1]
=> [2]
=> 0
[-1,-2,3] => [1,1]
=> [2]
=> 0
[-1,-2,-3] => [1,1,1]
=> [3]
=> 0
[1,3,-2] => [2]
=> [1,1]
=> 0
[1,-3,2] => [2]
=> [1,1]
=> 0
[-1,3,-2] => [2,1]
=> [2,1]
=> 1
[-1,-3,2] => [2,1]
=> [2,1]
=> 1
[2,-1,3] => [2]
=> [1,1]
=> 0
[2,-1,-3] => [2,1]
=> [2,1]
=> 1
[-2,1,3] => [2]
=> [1,1]
=> 0
[-2,1,-3] => [2,1]
=> [2,1]
=> 1
[2,3,-1] => [3]
=> [2,1]
=> 1
[2,-3,1] => [3]
=> [2,1]
=> 1
[-2,3,1] => [3]
=> [2,1]
=> 1
[-2,-3,-1] => [3]
=> [2,1]
=> 1
[3,1,-2] => [3]
=> [2,1]
=> 1
[3,-1,2] => [3]
=> [2,1]
=> 1
[-3,1,2] => [3]
=> [2,1]
=> 1
[-3,-1,-2] => [3]
=> [2,1]
=> 1
[3,2,-1] => [2]
=> [1,1]
=> 0
[3,-2,-1] => [2,1]
=> [2,1]
=> 1
[-3,2,1] => [2]
=> [1,1]
=> 0
[-3,-2,1] => [2,1]
=> [2,1]
=> 1
[1,2,-3,-4] => [1,1]
=> [2]
=> 0
[1,-2,3,-4] => [1,1]
=> [2]
=> 0
[1,-2,-3,4] => [1,1]
=> [2]
=> 0
[1,-2,-3,-4] => [1,1,1]
=> [3]
=> 0
[-1,2,3,-4] => [1,1]
=> [2]
=> 0
[-1,2,-3,4] => [1,1]
=> [2]
=> 0
[-1,2,-3,-4] => [1,1,1]
=> [3]
=> 0
[-1,-2,3,4] => [1,1]
=> [2]
=> 0
[-1,-2,3,-4] => [1,1,1]
=> [3]
=> 0
[-1,-2,-3,4] => [1,1,1]
=> [3]
=> 0
[-1,-2,-3,-4] => [1,1,1,1]
=> [4]
=> 1
[1,2,4,-3] => [2]
=> [1,1]
=> 0
[1,2,-4,3] => [2]
=> [1,1]
=> 0
[1,-2,4,-3] => [2,1]
=> [2,1]
=> 1
[1,-2,-4,3] => [2,1]
=> [2,1]
=> 1
[-1,2,4,-3] => [2,1]
=> [2,1]
=> 1
[-1,2,-4,3] => [2,1]
=> [2,1]
=> 1
[-1,-2,4,3] => [1,1]
=> [2]
=> 0
[-1,-2,4,-3] => [2,1,1]
=> [3,1]
=> 2
[-1,-2,-4,3] => [2,1,1]
=> [3,1]
=> 2
[-1,-2,-4,-3] => [1,1]
=> [2]
=> 0
[1,3,-2,4] => [2]
=> [1,1]
=> 0
[1,3,-2,-4] => [2,1]
=> [2,1]
=> 1
Description
The number of characters of the symmetric group whose value on the partition is even.
Matching statistic: St001207
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%
Values
[-1,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,-3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[1,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-1,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[2,-1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[2,-1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-2,1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-2,1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[2,3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[2,-3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,-3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[3,1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[3,-1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-3,1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-3,-1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[3,2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[3,-2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-3,2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-3,-2,1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,-2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,-2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 1 + 2
[1,2,4,-3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,2,-4,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,-2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-2,4,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-2,-4,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,3,-2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,-3,2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,3,2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,3,-2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-3,2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-3,-2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,3,4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,3,-4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-3,4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-3,-4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-1,3,4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,3,-4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-3,4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-3,-4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[1,4,2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,4,-2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-4,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-4,-2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-1,4,2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,4,-2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-4,2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-4,-2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[1,4,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,-4,3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,4,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,4,-3,2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-4,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-4,-3,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[2,1,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[2,-1,3,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[2,-1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[2,-1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[-2,1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[-2,1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[2,3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[2,3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[2,-3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[2,-3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-2,3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-2,-3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,-3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
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: St001582
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%
Values
[-1,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,-3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[1,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-1,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[2,-1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[2,-1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-2,1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-2,1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[2,3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[2,-3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,-3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[3,1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[3,-1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-3,1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-3,-1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[3,2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[3,-2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-3,2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[-3,-2,1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,-2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,-2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 2
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 1 + 2
[1,2,4,-3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,2,-4,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,-2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-2,4,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-2,-4,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,3,-2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,-3,2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,3,2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,3,-2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-3,2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-3,-2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[1,3,4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,3,-4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-3,4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-3,-4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-1,3,4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,3,-4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-3,4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-3,-4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[1,4,2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,4,-2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-4,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[1,-4,-2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-1,4,2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,4,-2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-4,2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-1,-4,-2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[1,4,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[1,-4,3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[1,-4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,4,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,4,-3,2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-4,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3 = 1 + 2
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-1,-4,-3,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[2,1,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2 = 0 + 2
[2,-1,3,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2 = 0 + 2
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 2
[2,-1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[2,-1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[-2,1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[-2,1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 2
[2,3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[2,3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[2,-3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[2,-3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-2,3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
[-2,-3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 2
[-2,-3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 2
Description
The grades of the simple modules corresponding to the points in the poset of the symmetric group under the Bruhat order.
Matching statistic: St001171
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 17% ●values known / values provided: 25%●distinct values known / distinct values provided: 17%
Values
[-1,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[-2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,-2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,-2,-3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 5
[1,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,-3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[-1,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[2,-1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[2,-1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-2,1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[-2,1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[2,3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[2,-3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-2,3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-2,-3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[3,1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[3,-1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-3,1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-3,-1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[3,2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[3,-2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-3,2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[-3,-2,1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[1,-2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 5
[-1,2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 5
[-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,-2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 5
[-1,-2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 0 + 5
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 1 + 5
[1,2,4,-3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,2,-4,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,-2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[1,-2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,-2,4,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[-1,-2,-4,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[1,3,-2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[1,-3,2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,-3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,3,2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,3,-2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[-1,-3,2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[-1,-3,-2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[1,3,4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[1,3,-4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[1,-3,4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[1,-3,-4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-1,3,4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-1,3,-4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-1,-3,4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-1,-3,-4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[1,4,2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[1,4,-2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[1,-4,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[1,-4,-2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-1,4,2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-1,4,-2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-1,-4,2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-1,-4,-2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[1,4,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[1,-4,3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[1,-4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,4,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,4,-3,2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[-1,-4,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 1 + 5
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[-1,-4,-3,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[2,1,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 0 + 5
[2,-1,3,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 0 + 5
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 2 + 5
[2,-1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 5
[2,-1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 5
[-2,1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 5
[-2,1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 1 + 5
[2,3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[2,3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[2,-3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[2,-3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-2,3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-2,3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
[-2,-3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 1 + 5
[-2,-3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 1 + 5
Description
The 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 $K[x]/(x^n)$.
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