searching the database
Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St000625
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000625: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000625: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[-1,-2] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[2,-1] => [2]
=> [[1,2]]
=> [1,2] => 2
[-2,1] => [2]
=> [[1,2]]
=> [1,2] => 2
[1,-2,-3] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[-1,2,-3] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[-1,-2,3] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[-1,-2,-3] => [1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 3
[1,3,-2] => [2]
=> [[1,2]]
=> [1,2] => 2
[1,-3,2] => [2]
=> [[1,2]]
=> [1,2] => 2
[-1,3,-2] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[-1,-3,2] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[2,-1,3] => [2]
=> [[1,2]]
=> [1,2] => 2
[2,-1,-3] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[-2,1,3] => [2]
=> [[1,2]]
=> [1,2] => 2
[-2,1,-3] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[2,3,-1] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[2,-3,1] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[-2,3,1] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[-2,-3,-1] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[3,1,-2] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[3,-1,2] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[-3,1,2] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[-3,-1,-2] => [3]
=> [[1,2,3]]
=> [1,2,3] => 3
[3,2,-1] => [2]
=> [[1,2]]
=> [1,2] => 2
[3,-2,-1] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[-3,2,1] => [2]
=> [[1,2]]
=> [1,2] => 2
[-3,-2,1] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[1,2,-3,-4] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[1,-2,3,-4] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[1,-2,-3,4] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[1,-2,-3,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 3
[-1,2,3,-4] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[-1,2,-3,4] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[-1,2,-3,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 3
[-1,-2,3,4] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[-1,-2,3,-4] => [1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 3
[-1,-2,-3,4] => [1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 3
[-1,-2,-3,-4] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => 4
[1,2,4,-3] => [2]
=> [[1,2]]
=> [1,2] => 2
[1,2,-4,3] => [2]
=> [[1,2]]
=> [1,2] => 2
[1,-2,4,-3] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[1,-2,-4,3] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[-1,2,4,-3] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[-1,2,-4,3] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
[-1,-2,4,3] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[-1,-2,4,-3] => [2,1,1]
=> [[1,4],[2],[3]]
=> [3,2,1,4] => 4
[-1,-2,-4,3] => [2,1,1]
=> [[1,4],[2],[3]]
=> [3,2,1,4] => 4
[-1,-2,-4,-3] => [1,1]
=> [[1],[2]]
=> [2,1] => 2
[1,3,-2,4] => [2]
=> [[1,2]]
=> [1,2] => 2
[1,3,-2,-4] => [2,1]
=> [[1,3],[2]]
=> [2,1,3] => 3
Description
The sum of the minimal distances to a greater element.
Set $\pi_0 = \pi_{n+1} = n+1$, then this statistic is
$$
\sum_{i=1}^n \min_d(\pi_{i-d}>\pi_i\text{ or }\pi_{i+d}>\pi_i)
$$
This statistic appears in [1].
The generating function for the sequence of maximal values attained on $\mathfrak S_r$, $r\geq 0$ apparently coincides with [2], which satisfies the functional equation
$$
(x-1)^2 (x+1)^3 f(x^2) - (x-1)^2 (x+1) f(x) + x = 0.
$$
Matching statistic: St001879
Mp00169: Signed permutations —odd cycle type⟶ Integer partitions
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 86%
Mp00179: Integer partitions —to skew partition⟶ Skew partitions
Mp00185: Skew partitions —cell poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 47% ●values known / values provided: 47%●distinct values known / distinct values provided: 86%
Values
[-1,-2] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[2,-1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-2,1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,-2,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,2,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,-2,3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,-2,-3] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,3,-2] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,-3,2] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,3,-2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-1,-3,2] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[2,-1,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[2,-1,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-2,1,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-2,1,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[2,3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[2,-3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-2,3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-2,-3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[3,1,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[3,-1,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-3,1,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-3,-1,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[3,2,-1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[3,-2,-1] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-3,2,1] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-3,-2,1] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[1,2,-3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,-2,3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,-2,-3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,-2,-3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-1,2,3,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,2,-3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,2,-3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-1,-2,3,4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,-2,3,-4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-1,-2,-3,4] => [1,1,1]
=> [[1,1,1],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-1,-2,-3,-4] => [1,1,1,1]
=> [[1,1,1,1],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[1,2,4,-3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,2,-4,3] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,-2,4,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[1,-2,-4,3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-1,2,4,-3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-1,2,-4,3] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-1,-2,4,3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,-2,4,-3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,-2,-4,3] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,-2,-4,-3] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,3,-2,4] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,3,-2,-4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[1,-3,2,4] => [2]
=> [[2],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,-3,2,-4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-1,3,2,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[-1,3,-2,4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-1,3,-2,-4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,-3,2,4] => [2,1]
=> [[2,1],[]]
=> ([(0,1),(0,2)],3)
=> ? = 3 - 1
[-1,-3,2,-4] => [2,1,1]
=> [[2,1,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,-3,-2,-4] => [1,1]
=> [[1,1],[]]
=> ([(0,1)],2)
=> ? = 2 - 1
[1,3,4,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,3,-4,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,-3,4,2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,-3,-4,-2] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-1,3,4,-2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,3,-4,2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,-3,4,2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,-3,-4,-2] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[1,4,2,-3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,4,-2,3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,-4,2,3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[1,-4,-2,-3] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-1,4,2,-3] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[-1,4,-2,3] => [3,1]
=> [[3,1],[]]
=> ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 1
[2,-1,4,-3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[2,-1,-4,3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[-2,1,4,-3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[-2,1,-4,3] => [2,2]
=> [[2,2],[]]
=> ([(0,1),(0,2),(1,3),(2,3)],4)
=> 4 = 5 - 1
[2,3,-1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[2,-3,1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-2,3,1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-2,-3,-1,4] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[2,3,4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,3,-4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,-3,4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,-3,-4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,3,4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,3,-4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,-3,4,-1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,-3,-4,1] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,4,1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,4,-1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,-4,1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,-4,-1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,4,1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,4,-1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,-4,1,-3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[-2,-4,-1,3] => [4]
=> [[4],[]]
=> ([(0,3),(2,1),(3,2)],4)
=> 3 = 4 - 1
[2,4,3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[2,-4,3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-2,4,3,1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
[-2,-4,3,-1] => [3]
=> [[3],[]]
=> ([(0,2),(2,1)],3)
=> 2 = 3 - 1
Description
The number of indecomposable summands of the top of the first syzygy of the dual of the regular module in the incidence algebra of the lattice.
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: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Values
[-1,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,-3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[1,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-1,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[2,-1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[2,-1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-2,1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-2,1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[2,3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,-3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,-3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[3,1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[3,-1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-3,1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-3,-1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[3,2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[3,-2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-3,2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-3,-2,1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,-2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,-2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 4
[1,2,4,-3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,2,-4,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,-2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-2,4,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-2,-4,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,3,-2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,-3,2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,3,2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,3,-2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-3,2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-3,-2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,3,4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,3,-4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-3,4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-3,-4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-1,3,4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,3,-4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-3,4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-3,-4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[1,4,2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,4,-2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-4,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-4,-2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-1,4,2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,4,-2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-4,2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-4,-2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[1,4,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,-4,3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,4,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,4,-3,2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-4,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-4,-3,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,1,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,-1,3,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[2,-1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[2,-1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[-2,1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[-2,1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[2,3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[2,-3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,-3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-2,3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-2,-3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,-3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
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: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Values
[-1,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,-3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[1,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-1,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[2,-1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[2,-1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-2,1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-2,1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[2,3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,-3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,-3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[3,1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[3,-1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-3,1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-3,-1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[3,2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[3,-2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-3,2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[-3,-2,1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,-2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,-2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 4
[1,2,4,-3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,2,-4,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,-2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-2,4,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-2,-4,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,3,-2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,-3,2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,3,2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,3,-2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-3,2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-3,-2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[1,3,4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,3,-4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-3,4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-3,-4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-1,3,4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,3,-4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-3,4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-3,-4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[1,4,2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,4,-2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-4,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[1,-4,-2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-1,4,2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,4,-2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-4,2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-1,-4,-2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[1,4,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[1,-4,3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[1,-4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,4,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,4,-3,2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-4,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 3
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-1,-4,-3,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,1,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 2
[2,-1,3,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 2
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4
[2,-1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[2,-1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[-2,1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[-2,1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5
[2,3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[2,-3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[2,-3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-2,3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
[-2,-3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3
[-2,-3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4
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: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 26% ●values known / values provided: 26%●distinct values known / distinct values provided: 29%
Values
[-1,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[-2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,-2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,2,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,-2,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,-2,-3] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3 + 3
[1,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,-3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[-1,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[2,-1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[2,-1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-2,1,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[-2,1,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[2,3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[2,-3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-2,3,1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-2,-3,-1] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[3,1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[3,-1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-3,1,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-3,-1,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[3,2,-1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[3,-2,-1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-3,2,1] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[-3,-2,1] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[1,2,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,-2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,-2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,-2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3 + 3
[-1,2,3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,2,-3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,2,-3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3 + 3
[-1,-2,3,4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,-2,3,-4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3 + 3
[-1,-2,-3,4] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [3,1,4,5,2] => ? = 3 + 3
[-1,-2,-3,-4] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [3,1,4,5,6,2] => ? = 4 + 3
[1,2,4,-3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,2,-4,3] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,-2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[1,-2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,2,4,-3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,2,-4,3] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,-2,4,3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,-2,4,-3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[-1,-2,-4,3] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[-1,-2,-4,-3] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,3,-2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,3,-2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[1,-3,2,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,-3,2,-4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,3,2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,3,-2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,3,-2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[-1,-3,2,4] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,-3,2,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[-1,-3,-2,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[1,3,4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,3,-4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,-3,4,2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,-3,-4,-2] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-1,3,4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-1,3,-4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-1,-3,4,2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-1,-3,-4,-2] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[1,4,2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,4,-2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,-4,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[1,-4,-2,-3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-1,4,2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-1,4,-2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-1,-4,2,3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-1,-4,-2,-3] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[1,4,3,-2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,4,-3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[1,-4,3,2] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[1,-4,-3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,4,3,-2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,4,-3,2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[-1,4,-3,-2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[-1,-4,3,2] => [2,1]
=> [1,0,1,0,1,0]
=> [4,1,2,3] => 6 = 3 + 3
[-1,-4,-3,2] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[-1,-4,-3,-2] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[2,1,-3,-4] => [1,1]
=> [1,0,1,1,0,0]
=> [3,1,4,2] => 5 = 2 + 3
[2,-1,3,4] => [2]
=> [1,1,0,0,1,0]
=> [2,4,1,3] => 5 = 2 + 3
[2,-1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[-2,1,-3,-4] => [2,1,1]
=> [1,0,1,1,0,1,0,0]
=> [5,1,4,2,3] => ? = 4 + 3
[2,-1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5 + 3
[2,-1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5 + 3
[-2,1,4,-3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5 + 3
[-2,1,-4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [2,4,1,5,3] => ? = 5 + 3
[2,3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[2,3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[2,-3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[2,-3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-2,3,1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-2,3,1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
[-2,-3,-1,4] => [3]
=> [1,1,1,0,0,0,1,0]
=> [2,3,5,1,4] => ? = 3 + 3
[-2,-3,-1,-4] => [3,1]
=> [1,1,0,1,0,0,1,0]
=> [5,3,1,2,4] => ? = 4 + 3
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 $K[x]/(x^n)$.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!