Processing math: 100%

Your data matches 5 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000030
(load all 2 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St000030: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => 0
{{1,2}}
 => [2,1] => [1,2] => 0
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => 0
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => 0
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => 1
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => 2
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => 2
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => 1
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => 2
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => 1
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => 3
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => 2
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => 2
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => 3
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => 1
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => 3
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => 1
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => 1
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => 3
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => 2
Description
The sum of the descent differences of a permutations. This statistic is given by π↦∑i∈Des(π)(πi−πi+1). See [[St000111]] and [[St000154]] for the sum of the descent tops and the descent bottoms, respectively. This statistic was studied in [1] and [2] where is was called the ''drop'' of a permutation.
Matching statistic: St000029
(load all 3 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
St000029: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1}}
 => [1] => [1] => [1] => 0
{{1,2}}
 => [2,1] => [1,2] => [1,2] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => [1,2,3] => 0
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => [1,2,3] => 0
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => [1,3,2] => 1
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => [1,2,3] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => [1,2,4,3] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => [1,4,3,2] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => [1,3,2,4] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => [1,3,4,2] => 2
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => [1,3,4,2] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4] => 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => [1,2,5,4,3] => 2
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => [1,2,4,5,3] => 2
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => [1,2,4,5,3] => 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => [1,2,3,5,4] => 1
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => [1,5,3,4,2] => 3
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => [1,4,3,2,5] => 2
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => [1,4,3,2,5] => 2
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => [1,4,3,5,2] => 3
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => [1,4,3,5,2] => 3
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => [1,3,2,5,4] => 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => 1
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => [1,3,5,4,2] => 3
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => [1,3,4,2,5] => 2
Description
The depth of a permutation. This is given by dp(σ)=∑σi>i(σi−i)=|{i≤j:σi>j}|. The depth is half of the total displacement [4], Problem 5.1.1.28, or Spearman’s disarray [3] ∑i|σi−i|. Permutations with depth at most 1 are called ''almost-increasing'' in [5].
Matching statistic: St001207
(load all 10 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 43%
Values
{{1}}
 => [1] => [1] => ? = 0
{{1,2}}
 => [2,1] => [1,2] => 0
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => 0
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => 0
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => 1
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => 2
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => ? = 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => ? = 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => ? = 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => ? = 0
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => ? = 2
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => ? = 1
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => ? = 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => ? = 2
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => ? = 0
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => ? = 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => ? = 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => ? = 1
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => ? = 0
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => ? = 3
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => ? = 2
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => ? = 2
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => ? = 3
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => ? = 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => ? = 1
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => ? = 3
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => ? = 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => ? = 1
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => ? = 1
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => ? = 3
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => ? = 2
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [1,4,2,3,5] => ? = 2
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => [1,5,2,3,4] => ? = 3
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,2,3,4,5] => ? = 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2,3},{4}}
 => [5,3,2,4,1] => [1,5,2,3,4] => ? = 3
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,2,3,5,4] => ? = 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,2,3,4,5] => ? = 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,2,3,4,5] => ? = 0
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [1,4,5,2,3] => ? = 3
{{1,4},{2,5},{3}}
 => [4,5,3,1,2] => [1,4,2,5,3] => ? = 4
{{1,4},{2},{3,5}}
 => [4,2,5,1,3] => [1,4,2,3,5] => ? = 2
{{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => [1,4,2,3,5] => ? = 2
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [1,5,2,4,3] => ? = 4
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,2,4,5,3] => ? = 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,2,4,3,5] => ? = 1
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,2,4,3,5] => ? = 1
{{1,5},{2},{3,4}}
 => [5,2,4,3,1] => [1,5,2,3,4] => ? = 3
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,2,5,3,4] => ? = 2
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,3,4,5] => ? = 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [1,5,2,3,4] => ? = 3
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,2,5,3,4] => ? = 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]/(xn).
Matching statistic: St001583
(load all 2 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St001583: Permutations ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 43%
Values
{{1}}
 => [1] => [1] => [1] => ? = 0
{{1,2}}
 => [2,1] => [1,2] => [2,1] => 0
{{1},{2}}
 => [1,2] => [1,2] => [2,1] => 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => [3,2,1] => 0
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => [3,2,1] => 0
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => [2,3,1] => 1
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => [3,2,1] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [3,2,1] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => [4,3,2,1] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => [4,3,2,1] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => [3,4,2,1] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => [4,3,2,1] => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => [4,3,2,1] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => [2,4,3,1] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => [4,2,3,1] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => [4,2,3,1] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => [3,2,4,1] => 2
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => [4,3,2,1] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => [4,3,2,1] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => [3,2,4,1] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => [3,4,2,1] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => [4,3,2,1] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => [4,5,3,2,1] => ? = 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => [3,5,4,2,1] => ? = 2
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => [5,3,4,2,1] => ? = 1
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => [5,3,4,2,1] => ? = 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => [4,3,5,2,1] => ? = 2
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => [4,3,5,2,1] => ? = 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => [4,5,3,2,1] => ? = 1
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => [2,5,4,3,1] => ? = 3
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => [5,2,4,3,1] => ? = 2
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => [5,2,4,3,1] => ? = 2
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => [4,2,5,3,1] => ? = 3
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => [5,4,2,3,1] => ? = 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => [5,4,2,3,1] => ? = 1
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => [4,2,5,3,1] => ? = 3
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => [4,5,2,3,1] => ? = 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => [5,4,2,3,1] => ? = 1
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => [5,4,2,3,1] => ? = 1
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => [3,2,5,4,1] => ? = 3
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => [5,3,2,4,1] => ? = 2
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => ? = 2
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => [1,5,2,3,4] => [4,3,2,5,1] => ? = 3
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,5},{2,3},{4}}
 => [5,3,2,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => ? = 3
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,2,3,5,4] => [4,5,3,2,1] => ? = 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [1,4,5,2,3] => [3,2,5,4,1] => ? = 3
{{1,4},{2,5},{3}}
 => [4,5,3,1,2] => [1,4,2,5,3] => [3,5,2,4,1] => ? = 4
{{1,4},{2},{3,5}}
 => [4,2,5,1,3] => [1,4,2,3,5] => [5,3,2,4,1] => ? = 2
{{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => [1,4,2,3,5] => [5,3,2,4,1] => ? = 2
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [1,5,2,4,3] => [3,4,2,5,1] => ? = 4
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,2,4,5,3] => [3,5,4,2,1] => ? = 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,2,4,3,5] => [5,3,4,2,1] => ? = 1
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,2,4,3,5] => [5,3,4,2,1] => ? = 1
{{1,5},{2},{3,4}}
 => [5,2,4,3,1] => [1,5,2,3,4] => [4,3,2,5,1] => ? = 3
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,2,5,3,4] => [4,3,5,2,1] => ? = 2
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,3,4,5] => [5,4,3,2,1] => ? = 0
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [1,5,2,3,4] => [4,3,2,5,1] => ? = 3
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,2,5,3,4] => [4,3,5,2,1] => ? = 2
Description
The projective dimension of the simple module corresponding to the point in the poset of the symmetric group under bruhat order.
Matching statistic: St001860
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00090: Permutations —cycle-as-one-line notation⟶ Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
St001860: Signed permutations ⟶ ℤResult quality: 8% ●values known / values provided: 8%●distinct values known / distinct values provided: 43%
Values
{{1}}
 => [1] => [1] => [1] => ? = 0
{{1,2}}
 => [2,1] => [1,2] => [1,2] => 0
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [1,2,3] => [1,2,3] => 0
{{1,2},{3}}
 => [2,1,3] => [1,2,3] => [1,2,3] => 0
{{1,3},{2}}
 => [3,2,1] => [1,3,2] => [1,3,2] => 1
{{1},{2,3}}
 => [1,3,2] => [1,2,3] => [1,2,3] => 0
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3},{4}}
 => [2,3,1,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,4},{3}}
 => [2,4,3,1] => [1,2,4,3] => [1,2,4,3] => 1
{{1,2},{3,4}}
 => [2,1,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2},{3},{4}}
 => [2,1,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,3,4},{2}}
 => [3,2,4,1] => [1,3,4,2] => [1,3,4,2] => 2
{{1,3},{2,4}}
 => [3,4,1,2] => [1,3,2,4] => [1,3,2,4] => 1
{{1,3},{2},{4}}
 => [3,2,1,4] => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2,3}}
 => [4,3,2,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,3,4}}
 => [1,3,4,2] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,4},{2},{3}}
 => [4,2,3,1] => [1,4,2,3] => [1,4,2,3] => 2
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,3,4] => [1,2,3,4] => 0
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
{{1,2,3,4,5}}
 => [2,3,4,5,1] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,3,4},{5}}
 => [2,3,4,1,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,3,5},{4}}
 => [2,3,5,4,1] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 1
{{1,2,3},{4,5}}
 => [2,3,1,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,3},{4},{5}}
 => [2,3,1,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,4,5},{3}}
 => [2,4,3,5,1] => [1,2,4,5,3] => [1,2,4,5,3] => ? = 2
{{1,2,4},{3,5}}
 => [2,4,5,1,3] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 1
{{1,2,4},{3},{5}}
 => [2,4,3,1,5] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 1
{{1,2,5},{3,4}}
 => [2,5,4,3,1] => [1,2,5,3,4] => [1,2,5,3,4] => ? = 2
{{1,2},{3,4,5}}
 => [2,1,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2},{3,4},{5}}
 => [2,1,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2,5},{3},{4}}
 => [2,5,3,4,1] => [1,2,5,3,4] => [1,2,5,3,4] => ? = 2
{{1,2},{3,5},{4}}
 => [2,1,5,4,3] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 1
{{1,2},{3},{4,5}}
 => [2,1,3,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,2},{3},{4},{5}}
 => [2,1,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,3,4,5},{2}}
 => [3,2,4,5,1] => [1,3,4,5,2] => [1,3,4,5,2] => ? = 3
{{1,3,4},{2,5}}
 => [3,5,4,1,2] => [1,3,4,2,5] => [1,3,4,2,5] => ? = 2
{{1,3,4},{2},{5}}
 => [3,2,4,1,5] => [1,3,4,2,5] => [1,3,4,2,5] => ? = 2
{{1,3,5},{2,4}}
 => [3,4,5,2,1] => [1,3,5,2,4] => [1,3,5,2,4] => ? = 3
{{1,3},{2,4,5}}
 => [3,4,1,5,2] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 1
{{1,3},{2,4},{5}}
 => [3,4,1,2,5] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 1
{{1,3,5},{2},{4}}
 => [3,2,5,4,1] => [1,3,5,2,4] => [1,3,5,2,4] => ? = 3
{{1,3},{2,5},{4}}
 => [3,5,1,4,2] => [1,3,2,5,4] => [1,3,2,5,4] => ? = 2
{{1,3},{2},{4,5}}
 => [3,2,1,5,4] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 1
{{1,3},{2},{4},{5}}
 => [3,2,1,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 1
{{1,4,5},{2,3}}
 => [4,3,2,5,1] => [1,4,5,2,3] => [1,4,5,2,3] => ? = 3
{{1,4},{2,3,5}}
 => [4,3,5,1,2] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,4},{2,3},{5}}
 => [4,3,2,1,5] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,5},{2,3,4}}
 => [5,3,4,2,1] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 3
{{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2,3},{4}}
 => [5,3,2,4,1] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 3
{{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 1
{{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,4,5},{2},{3}}
 => [4,2,3,5,1] => [1,4,5,2,3] => [1,4,5,2,3] => ? = 3
{{1,4},{2,5},{3}}
 => [4,5,3,1,2] => [1,4,2,5,3] => [1,4,2,5,3] => ? = 4
{{1,4},{2},{3,5}}
 => [4,2,5,1,3] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,4},{2},{3},{5}}
 => [4,2,3,1,5] => [1,4,2,3,5] => [1,4,2,3,5] => ? = 2
{{1,5},{2,4},{3}}
 => [5,4,3,2,1] => [1,5,2,4,3] => [1,5,2,4,3] => ? = 4
{{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,2,4,5,3] => [1,2,4,5,3] => ? = 2
{{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 1
{{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 1
{{1,5},{2},{3,4}}
 => [5,2,4,3,1] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 3
{{1},{2,5},{3,4}}
 => [1,5,4,3,2] => [1,2,5,3,4] => [1,2,5,3,4] => ? = 2
{{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
{{1,5},{2},{3},{4}}
 => [5,2,3,4,1] => [1,5,2,3,4] => [1,5,2,3,4] => ? = 3
{{1},{2,5},{3},{4}}
 => [1,5,3,4,2] => [1,2,5,3,4] => [1,2,5,3,4] => ? = 2
Description
The number of factors of the Stanley symmetric function associated with a signed permutation.