Your data matches 4 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000202
Mapping
St000202: Cores ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([2],3)
 => 3
([1,1],3)
 => 3
([3,1],3)
 => 5
([2,1,1],3)
 => 5
([4,2],3)
 => 6
([3,1,1],3)
 => 7
([2,2,1,1],3)
 => 6
([5,3,1],3)
 => 9
([4,2,1,1],3)
 => 10
([3,2,2,1,1],3)
 => 9
([2],4)
 => 3
([1,1],4)
 => 3
([3],4)
 => 4
([2,1],4)
 => 5
([1,1,1],4)
 => 4
([4,1],4)
 => 7
([2,2],4)
 => 6
([3,1,1],4)
 => 8
([2,1,1,1],4)
 => 7
([5,2],4)
 => 9
([4,1,1],4)
 => 10
([3,2,1],4)
 => 10
([3,1,1,1],4)
 => 10
([2,2,1,1,1],4)
 => 9
([6,3],4)
 => 10
([5,2,1],4)
 => 14
([4,1,1,1],4)
 => 13
([4,2,2],4)
 => 13
([3,3,1,1],4)
 => 13
([3,2,1,1,1],4)
 => 14
([2,2,2,1,1,1],4)
 => 10
([2],5)
 => 3
([1,1],5)
 => 3
([3],5)
 => 4
([2,1],5)
 => 5
([1,1,1],5)
 => 4
([4],5)
 => 5
([3,1],5)
 => 7
([2,2],5)
 => 6
([2,1,1],5)
 => 7
([1,1,1,1],5)
 => 5
([5,1],5)
 => 9
([3,2],5)
 => 9
([4,1,1],5)
 => 11
([2,2,1],5)
 => 9
([3,1,1,1],5)
 => 11
([2,1,1,1,1],5)
 => 9
([6,2],5)
 => 12
([5,1,1],5)
 => 13
([3,3],5)
 => 10
Description
The number of k-cores contained in the k-core. Let $\lambda$ and $\mu$ be $k$-cores. Then $\lambda$ contains $\mu$ if and only if the Ferrers diagram of $\lambda$ contains the diagram of $\mu$. Each nonempty core trivially contains two other cores, the empty core and itself. The poset corresponding to containment is Young's lattice restricted to cores [1].
Matching statistic: St001207
Mapping
Mp00022: Cores —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 12%
Values
([2],3)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],3)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3,1],3)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? ∊ {5,5} - 1
([2,1,1],3)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {5,5} - 1
([4,2],3)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => ? ∊ {6,6,7} - 1
([3,1,1],3)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? ∊ {6,6,7} - 1
([2,2,1,1],3)
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => ? ∊ {6,6,7} - 1
([5,3,1],3)
 => [5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [7,3,5,1,2,4,6] => ? ∊ {9,9,10} - 1
([4,2,1,1],3)
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [6,1,4,2,3,5] => ? ∊ {9,9,10} - 1
([3,2,2,1,1],3)
 => [3,2,2,1,1]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [7,1,5,2,6,3,4] => ? ∊ {9,9,10} - 1
([2],4)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],4)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3],4)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} - 1
([2,1],4)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 4 - 1
([1,1,1],4)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} - 1
([4,1],4)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => ? ∊ {6,7,7,8} - 1
([2,2],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? ∊ {6,7,7,8} - 1
([3,1,1],4)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? ∊ {6,7,7,8} - 1
([2,1,1,1],4)
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => ? ∊ {6,7,7,8} - 1
([5,2],4)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? ∊ {9,9,10,10,10} - 1
([4,1,1],4)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => ? ∊ {9,9,10,10,10} - 1
([3,2,1],4)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => ? ∊ {9,9,10,10,10} - 1
([3,1,1,1],4)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {9,9,10,10,10} - 1
([2,2,1,1,1],4)
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [6,1,4,5,2,7,3] => ? ∊ {9,9,10,10,10} - 1
([6,3],4)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [2,3,8,5,6,1,4,7] => ? ∊ {10,10,13,13,13,14,14} - 1
([5,2,1],4)
 => [5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [7,5,4,1,2,3,6] => ? ∊ {10,10,13,13,13,14,14} - 1
([4,1,1,1],4)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => ? ∊ {10,10,13,13,13,14,14} - 1
([4,2,2],4)
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => ? ∊ {10,10,13,13,13,14,14} - 1
([3,3,1,1],4)
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [3,1,5,2,6,4] => ? ∊ {10,10,13,13,13,14,14} - 1
([3,2,1,1,1],4)
 => [3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [7,1,6,5,2,3,4] => ? ∊ {10,10,13,13,13,14,14} - 1
([2,2,2,1,1,1],4)
 => [2,2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [6,1,4,5,2,7,8,3] => ? ∊ {10,10,13,13,13,14,14} - 1
([2],5)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],5)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3],5)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} - 1
([2,1],5)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 4 - 1
([1,1,1],5)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} - 1
([4],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => ? ∊ {5,5,6,7,7} - 1
([3,1],5)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? ∊ {5,5,6,7,7} - 1
([2,2],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? ∊ {5,5,6,7,7} - 1
([2,1,1],5)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {5,5,6,7,7} - 1
([1,1,1,1],5)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => ? ∊ {5,5,6,7,7} - 1
([5,1],5)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? ∊ {9,9,9,9,11,11} - 1
([3,2],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => ? ∊ {9,9,9,9,11,11} - 1
([4,1,1],5)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => ? ∊ {9,9,9,9,11,11} - 1
([2,2,1],5)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? ∊ {9,9,9,9,11,11} - 1
([3,1,1,1],5)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {9,9,9,9,11,11} - 1
([2,1,1,1,1],5)
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [7,1,4,5,6,2,3] => ? ∊ {9,9,9,9,11,11} - 1
([6,2],5)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [2,8,4,5,6,1,3,7] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([5,1,1],5)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([3,3],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([4,2,1],5)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([4,1,1,1],5)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([2,2,2],5)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([3,2,1,1],5)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([3,1,1,1,1],5)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([2,2,1,1,1,1],5)
 => [2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [7,1,4,5,6,2,8,3] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([2],6)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],6)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3],6)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} - 1
([2,1],6)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 4 - 1
([1,1,1],6)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} - 1
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
Mapping
Mp00022: Cores —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001582: Permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 12%
Values
([2],3)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],3)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3,1],3)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? ∊ {5,5} - 1
([2,1,1],3)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {5,5} - 1
([4,2],3)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => ? ∊ {6,6,7} - 1
([3,1,1],3)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? ∊ {6,6,7} - 1
([2,2,1,1],3)
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => ? ∊ {6,6,7} - 1
([5,3,1],3)
 => [5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [7,3,5,1,2,4,6] => ? ∊ {9,9,10} - 1
([4,2,1,1],3)
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [6,1,4,2,3,5] => ? ∊ {9,9,10} - 1
([3,2,2,1,1],3)
 => [3,2,2,1,1]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [7,1,5,2,6,3,4] => ? ∊ {9,9,10} - 1
([2],4)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],4)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3],4)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} - 1
([2,1],4)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 4 - 1
([1,1,1],4)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} - 1
([4,1],4)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => ? ∊ {6,7,7,8} - 1
([2,2],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? ∊ {6,7,7,8} - 1
([3,1,1],4)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? ∊ {6,7,7,8} - 1
([2,1,1,1],4)
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => ? ∊ {6,7,7,8} - 1
([5,2],4)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? ∊ {9,9,10,10,10} - 1
([4,1,1],4)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => ? ∊ {9,9,10,10,10} - 1
([3,2,1],4)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => ? ∊ {9,9,10,10,10} - 1
([3,1,1,1],4)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {9,9,10,10,10} - 1
([2,2,1,1,1],4)
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [6,1,4,5,2,7,3] => ? ∊ {9,9,10,10,10} - 1
([6,3],4)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [2,3,8,5,6,1,4,7] => ? ∊ {10,10,13,13,13,14,14} - 1
([5,2,1],4)
 => [5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [7,5,4,1,2,3,6] => ? ∊ {10,10,13,13,13,14,14} - 1
([4,1,1,1],4)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => ? ∊ {10,10,13,13,13,14,14} - 1
([4,2,2],4)
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => ? ∊ {10,10,13,13,13,14,14} - 1
([3,3,1,1],4)
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [3,1,5,2,6,4] => ? ∊ {10,10,13,13,13,14,14} - 1
([3,2,1,1,1],4)
 => [3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [7,1,6,5,2,3,4] => ? ∊ {10,10,13,13,13,14,14} - 1
([2,2,2,1,1,1],4)
 => [2,2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [6,1,4,5,2,7,8,3] => ? ∊ {10,10,13,13,13,14,14} - 1
([2],5)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],5)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3],5)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} - 1
([2,1],5)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 4 - 1
([1,1,1],5)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} - 1
([4],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => ? ∊ {5,5,6,7,7} - 1
([3,1],5)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? ∊ {5,5,6,7,7} - 1
([2,2],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? ∊ {5,5,6,7,7} - 1
([2,1,1],5)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {5,5,6,7,7} - 1
([1,1,1,1],5)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => ? ∊ {5,5,6,7,7} - 1
([5,1],5)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? ∊ {9,9,9,9,11,11} - 1
([3,2],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => ? ∊ {9,9,9,9,11,11} - 1
([4,1,1],5)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => ? ∊ {9,9,9,9,11,11} - 1
([2,2,1],5)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? ∊ {9,9,9,9,11,11} - 1
([3,1,1,1],5)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {9,9,9,9,11,11} - 1
([2,1,1,1,1],5)
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [7,1,4,5,6,2,3] => ? ∊ {9,9,9,9,11,11} - 1
([6,2],5)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [2,8,4,5,6,1,3,7] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([5,1,1],5)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([3,3],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([4,2,1],5)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([4,1,1,1],5)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([2,2,2],5)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([3,2,1,1],5)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([3,1,1,1,1],5)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([2,2,1,1,1,1],5)
 => [2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [7,1,4,5,6,2,8,3] => ? ∊ {10,10,12,12,13,13,14,15,15} - 1
([2],6)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 2 = 3 - 1
([1,1],6)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 2 = 3 - 1
([3],6)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} - 1
([2,1],6)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 3 = 4 - 1
([1,1,1],6)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} - 1
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
Mapping
Mp00022: Cores —to partition⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00201: Dyck paths —Ringel⟶ Permutations
St001171: Permutations ⟶ ℤResult quality: 11% ●values known / values provided: 11%●distinct values known / distinct values provided: 12%
Values
([2],3)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 5 = 3 + 2
([1,1],3)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 5 = 3 + 2
([3,1],3)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? ∊ {5,5} + 2
([2,1,1],3)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {5,5} + 2
([4,2],3)
 => [4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [2,6,4,1,3,5] => ? ∊ {6,6,7} + 2
([3,1,1],3)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? ∊ {6,6,7} + 2
([2,2,1,1],3)
 => [2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [5,1,4,2,6,3] => ? ∊ {6,6,7} + 2
([5,3,1],3)
 => [5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [7,3,5,1,2,4,6] => ? ∊ {9,9,10} + 2
([4,2,1,1],3)
 => [4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [6,1,4,2,3,5] => ? ∊ {9,9,10} + 2
([3,2,2,1,1],3)
 => [3,2,2,1,1]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [7,1,5,2,6,3,4] => ? ∊ {9,9,10} + 2
([2],4)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 5 = 3 + 2
([1,1],4)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 5 = 3 + 2
([3],4)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} + 2
([2,1],4)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 6 = 4 + 2
([1,1,1],4)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} + 2
([4,1],4)
 => [4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [6,3,4,1,2,5] => ? ∊ {6,7,7,8} + 2
([2,2],4)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? ∊ {6,7,7,8} + 2
([3,1,1],4)
 => [3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [3,1,5,2,4] => ? ∊ {6,7,7,8} + 2
([2,1,1,1],4)
 => [2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [6,1,4,5,2,3] => ? ∊ {6,7,7,8} + 2
([5,2],4)
 => [5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [2,7,4,5,1,3,6] => ? ∊ {9,9,10,10,10} + 2
([4,1,1],4)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => ? ∊ {9,9,10,10,10} + 2
([3,2,1],4)
 => [3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [5,1,2,3,4] => ? ∊ {9,9,10,10,10} + 2
([3,1,1,1],4)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {9,9,10,10,10} + 2
([2,2,1,1,1],4)
 => [2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [6,1,4,5,2,7,3] => ? ∊ {9,9,10,10,10} + 2
([6,3],4)
 => [6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [2,3,8,5,6,1,4,7] => ? ∊ {10,10,13,13,13,14,14} + 2
([5,2,1],4)
 => [5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [7,5,4,1,2,3,6] => ? ∊ {10,10,13,13,13,14,14} + 2
([4,1,1,1],4)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => ? ∊ {10,10,13,13,13,14,14} + 2
([4,2,2],4)
 => [4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,4,1,6,3,5] => ? ∊ {10,10,13,13,13,14,14} + 2
([3,3,1,1],4)
 => [3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [3,1,5,2,6,4] => ? ∊ {10,10,13,13,13,14,14} + 2
([3,2,1,1,1],4)
 => [3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [7,1,6,5,2,3,4] => ? ∊ {10,10,13,13,13,14,14} + 2
([2,2,2,1,1,1],4)
 => [2,2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [6,1,4,5,2,7,8,3] => ? ∊ {10,10,13,13,13,14,14} + 2
([2],5)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 5 = 3 + 2
([1,1],5)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 5 = 3 + 2
([3],5)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} + 2
([2,1],5)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 6 = 4 + 2
([1,1,1],5)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} + 2
([4],5)
 => [4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [2,3,4,6,1,5] => ? ∊ {5,5,6,7,7} + 2
([3,1],5)
 => [3,1]
 => [1,1,0,1,0,0,1,0]
 => [5,3,1,2,4] => ? ∊ {5,5,6,7,7} + 2
([2,2],5)
 => [2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,4,1,5,3] => ? ∊ {5,5,6,7,7} + 2
([2,1,1],5)
 => [2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [5,1,4,2,3] => ? ∊ {5,5,6,7,7} + 2
([1,1,1,1],5)
 => [1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [3,1,4,5,6,2] => ? ∊ {5,5,6,7,7} + 2
([5,1],5)
 => [5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [7,3,4,5,1,2,6] => ? ∊ {9,9,9,9,11,11} + 2
([3,2],5)
 => [3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,5,1,3,4] => ? ∊ {9,9,9,9,11,11} + 2
([4,1,1],5)
 => [4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,3,1,6,2,5] => ? ∊ {9,9,9,9,11,11} + 2
([2,2,1],5)
 => [2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [4,1,2,5,3] => ? ∊ {9,9,9,9,11,11} + 2
([3,1,1,1],5)
 => [3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [3,1,6,5,2,4] => ? ∊ {9,9,9,9,11,11} + 2
([2,1,1,1,1],5)
 => [2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [7,1,4,5,6,2,3] => ? ∊ {9,9,9,9,11,11} + 2
([6,2],5)
 => [6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [2,8,4,5,6,1,3,7] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([5,1,1],5)
 => [5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,3,4,1,7,2,6] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([3,3],5)
 => [3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [2,3,5,1,6,4] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([4,2,1],5)
 => [4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [6,4,1,2,3,5] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([4,1,1,1],5)
 => [4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [3,1,4,6,2,5] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([2,2,2],5)
 => [2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,4,1,5,6,3] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([3,2,1,1],5)
 => [3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [6,1,5,2,3,4] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([3,1,1,1,1],5)
 => [3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [3,1,7,5,6,2,4] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([2,2,1,1,1,1],5)
 => [2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [7,1,4,5,6,2,8,3] => ? ∊ {10,10,12,12,13,13,14,15,15} + 2
([2],6)
 => [2]
 => [1,1,0,0,1,0]
 => [2,4,1,3] => 5 = 3 + 2
([1,1],6)
 => [1,1]
 => [1,0,1,1,0,0]
 => [3,1,4,2] => 5 = 3 + 2
([3],6)
 => [3]
 => [1,1,1,0,0,0,1,0]
 => [2,3,5,1,4] => ? ∊ {4,5} + 2
([2,1],6)
 => [2,1]
 => [1,0,1,0,1,0]
 => [4,1,2,3] => 6 = 4 + 2
([1,1,1],6)
 => [1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [3,1,4,5,2] => ? ∊ {4,5} + 2
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 $K[x]/(x^n)$.