Your data matches 21 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000503
(load all 17 compositions to match this statistic)
Mapping
St000503: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => 1
{{1},{2}}
 => 0
{{1,2,3}}
 => 2
{{1,2},{3}}
 => 1
{{1,3},{2}}
 => 2
{{1},{2,3}}
 => 1
{{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => 3
{{1,2,3},{4}}
 => 2
{{1,2,4},{3}}
 => 3
{{1,2},{3,4}}
 => 1
{{1,2},{3},{4}}
 => 1
{{1,3,4},{2}}
 => 3
{{1,3},{2,4}}
 => 2
{{1,3},{2},{4}}
 => 2
{{1,4},{2,3}}
 => 3
{{1},{2,3,4}}
 => 2
{{1},{2,3},{4}}
 => 1
{{1,4},{2},{3}}
 => 3
{{1},{2,4},{3}}
 => 2
{{1},{2},{3,4}}
 => 1
{{1},{2},{3},{4}}
 => 0
Description
The maximal difference between two elements in a common block.
Matching statistic: St000209
(load all 14 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
St000209: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => 1
{{1},{2}}
 => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => 2
{{1,2},{3}}
 => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => 2
{{1},{2,3}}
 => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => 0
Description
Maximum difference of elements in cycles. Given a cycle $C$ in a permutation, we can compute the maximum distance between elements in the cycle, that is $\max \{ a_i-a_j | a_i, a_j \in C \}$. The statistic is then the maximum of this value over all cycles in the permutation.
Matching statistic: St000956
(load all 15 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
St000956: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => 1
{{1},{2}}
 => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => 2
{{1,2},{3}}
 => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => 2
{{1},{2,3}}
 => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => 0
Description
The maximal displacement of a permutation. This is $\max\{ |\pi(i)-i| \mid 1 \leq i \leq n\}$ for a permutation $\pi$ of $\{1,\ldots,n\}$. This statistic without the absolute value is the maximal drop size [[St000141]].
Matching statistic: St000141
(load all 16 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
St000141: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [3,1,2] => 2
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,2,3,1] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [4,2,1,3] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [4,3,2,1] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [2,4,3,1] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,1,2,4] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [4,1,2,3] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,3,1,2] => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,2,3] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
Description
The maximum drop size of a permutation. The maximum drop size of a permutation $\pi$ of $[n]=\{1,2,\ldots, n\}$ is defined to be the maximum value of $i-\pi(i)$.
Matching statistic: St000171
(load all 2 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000171: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => ([(0,1)],2)
 => 1
{{1},{2}}
 => [1,2] => ([],2)
 => 0
{{1,2,3}}
 => [2,3,1] => ([(0,2),(1,2)],3)
 => 2
{{1,2},{3}}
 => [2,1,3] => ([(1,2)],3)
 => 1
{{1,3},{2}}
 => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
{{1},{2,3}}
 => [1,3,2] => ([(1,2)],3)
 => 1
{{1},{2},{3}}
 => [1,2,3] => ([],3)
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 3
{{1,2,3},{4}}
 => [2,3,1,4] => ([(1,3),(2,3)],4)
 => 2
{{1,2,4},{3}}
 => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
{{1,2},{3,4}}
 => [2,1,4,3] => ([(0,3),(1,2)],4)
 => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => ([(2,3)],4)
 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 3
{{1,3},{2,4}}
 => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => 2
{{1,4},{2,3}}
 => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
{{1},{2,3,4}}
 => [1,3,4,2] => ([(1,3),(2,3)],4)
 => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => ([(2,3)],4)
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => ([(2,3)],4)
 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => ([],4)
 => 0
Description
The degree of the graph. This is the maximal vertex degree of a graph.
Matching statistic: St000316
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
St000316: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [2,3,1] => [3,1,2] => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [3,2,1] => 2
{{1},{2,3}}
 => [1,3,2] => [3,1,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [2,3,4,1] => [4,1,2,3] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [2,3,1,4] => [3,1,2,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [4,2,3,1] => [4,1,3,2] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [2,4,1,3] => [1,3,4,2] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [3,2,4,1] => [4,2,1,3] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [3,1,4,2] => [3,4,1,2] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => [3,2,1,4] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [4,3,2,1] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [3,4,1,2] => [1,4,2,3] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [3,1,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,4,3,1] => [4,2,3,1] => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => [4,3,1,2] => [1,4,3,2] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [4,1,2,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
Description
The number of non-left-to-right-maxima of a permutation. An integer $\sigma_i$ in the one-line notation of a permutation $\sigma$ is a **non-left-to-right-maximum** if there exists a $j < i$ such that $\sigma_j > \sigma_i$.
Matching statistic: St000442
(load all 2 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
St000442: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => [1,1,0,0]
 => 1
{{1},{2}}
 => [1,2] => [1,2] => [1,0,1,0]
 => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => [1,1,1,0,0,0]
 => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [1,1,0,0,1,0]
 => 1
{{1,3},{2}}
 => [3,2,1] => [3,1,2] => [1,1,1,0,0,0]
 => 2
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [1,0,1,1,0,0]
 => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,0,1,0,1,0]
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0]
 => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => [1,1,1,0,0,0,1,0]
 => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [4,2,1,3] => [1,1,1,1,0,0,0,0]
 => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0]
 => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0]
 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0]
 => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [2,4,3,1] => [1,1,0,1,1,0,0,0]
 => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0]
 => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0]
 => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => [1,0,1,1,1,0,0,0]
 => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0]
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,3,1,2] => [1,1,1,1,0,0,0,0]
 => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,2,3] => [1,0,1,1,1,0,0,0]
 => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0]
 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0]
 => 0
Description
The maximal area to the right of an up step of a Dyck path.
Matching statistic: St000651
(load all 3 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
Mp00064: Permutations —reverse⟶ Permutations
St000651: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => [1,2] => 1
{{1},{2}}
 => [1,2] => [1,2] => [2,1] => 0
{{1,2,3}}
 => [2,3,1] => [3,1,2] => [2,1,3] => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [3,1,2] => 1
{{1,3},{2}}
 => [3,2,1] => [2,3,1] => [1,3,2] => 2
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [2,3,1] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [3,2,1] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => [3,2,1,4] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [3,1,2,4] => [4,2,1,3] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [3,4,1,2] => [2,1,4,3] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [3,4,1,2] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [4,3,1,2] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [2,4,1,3] => [3,1,4,2] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [3,1,4,2] => [2,4,1,3] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [2,3,1,4] => [4,1,3,2] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [3,2,4,1] => [1,4,2,3] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,2,3] => [3,2,4,1] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [4,2,3,1] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [2,3,4,1] => [1,4,3,2] => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,3,4,2] => [2,4,3,1] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [3,4,2,1] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 0
Description
The maximal size of a rise in a permutation. This is $\max_i \sigma_{i+1}-\sigma_i$, except for the permutations without rises, where it is $0$.
Matching statistic: St000730
(load all 2 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000730: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => {{1,2}}
 => 1
{{1},{2}}
 => [1,2] => [1,2] => {{1},{2}}
 => 0
{{1,2,3}}
 => [2,3,1] => [3,2,1] => {{1,3},{2}}
 => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => {{1,2},{3}}
 => 1
{{1,3},{2}}
 => [3,2,1] => [3,1,2] => {{1,3},{2}}
 => 2
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => {{1},{2,3}}
 => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => {{1},{2},{3}}
 => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,2,3,1] => {{1,4},{2},{3}}
 => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [3,2,1,4] => {{1,3},{2},{4}}
 => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [4,2,1,3] => {{1,4},{2},{3}}
 => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => {{1,2},{3,4}}
 => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => {{1,2},{3},{4}}
 => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [4,3,2,1] => {{1,4},{2,3}}
 => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [2,4,3,1] => {{1,2,4},{3}}
 => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,1,2,4] => {{1,3},{2},{4}}
 => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [4,1,2,3] => {{1,4},{2},{3}}
 => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,3,2] => {{1},{2,4},{3}}
 => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => {{1},{2,3},{4}}
 => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,3,1,2] => {{1,4},{2,3}}
 => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,2,3] => {{1},{2,4},{3}}
 => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => {{1},{2},{3,4}}
 => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => {{1},{2},{3},{4}}
 => 0
Description
The maximal arc length of a set partition. The arcs of a set partition are those $i < j$ that are consecutive elements in the blocks. If there are no arcs, the maximal arc length is $0$.
Matching statistic: St001207
(load all 5 compositions to match this statistic)
Mapping
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
{{1,2}}
 => [2,1] => [2,1] => [2,1] => 1
{{1},{2}}
 => [1,2] => [1,2] => [1,2] => 0
{{1,2,3}}
 => [2,3,1] => [3,1,2] => [3,2,1] => 2
{{1,2},{3}}
 => [2,1,3] => [2,1,3] => [2,1,3] => 1
{{1,3},{2}}
 => [3,2,1] => [3,2,1] => [2,3,1] => 2
{{1},{2,3}}
 => [1,3,2] => [1,3,2] => [1,3,2] => 1
{{1},{2},{3}}
 => [1,2,3] => [1,2,3] => [1,2,3] => 0
{{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => [4,3,2,1] => 3
{{1,2,3},{4}}
 => [2,3,1,4] => [3,1,2,4] => [3,2,1,4] => 2
{{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => [3,4,2,1] => 3
{{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
{{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
{{1,3,4},{2}}
 => [3,2,4,1] => [4,2,1,3] => [2,4,3,1] => 3
{{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => [3,1,4,2] => 2
{{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => [2,3,1,4] => 2
{{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => [3,2,4,1] => 3
{{1},{2,3,4}}
 => [1,3,4,2] => [1,4,2,3] => [1,4,3,2] => 2
{{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
{{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => [2,3,4,1] => 3
{{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => [1,3,4,2] => 2
{{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
{{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
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 $K[x]/(x^n)$.
The following 11 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St000013The height of a Dyck path. St000058The order of a permutation. St000444The length of the maximal rise of a Dyck path. St000485The length of the longest cycle of a permutation. St000839The largest opener of a set partition. St000844The size of the largest block in the direct sum decomposition of a permutation. St001232The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2. St000454The largest eigenvalue of a graph if it is integral. St001330The hat guessing number of a graph. St001060The distinguishing index of a graph. St001880The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.