Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000209
(load all 3 compositions to match this statistic)
Mapping
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
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] => {{1}}
 => [1] => 0
[1,2] => {{1},{2}}
 => [1,2] => 0
[2,1] => {{1,2}}
 => [2,1] => 1
[1,2,3] => {{1},{2},{3}}
 => [1,2,3] => 0
[1,3,2] => {{1},{2,3}}
 => [1,3,2] => 1
[2,1,3] => {{1,2},{3}}
 => [2,1,3] => 1
[2,3,1] => {{1,2,3}}
 => [2,3,1] => 2
[3,1,2] => {{1,3},{2}}
 => [3,2,1] => 2
[3,2,1] => {{1,3},{2}}
 => [3,2,1] => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => [1,2,3,4] => 0
[1,2,4,3] => {{1},{2},{3,4}}
 => [1,2,4,3] => 1
[1,3,2,4] => {{1},{2,3},{4}}
 => [1,3,2,4] => 1
[1,3,4,2] => {{1},{2,3,4}}
 => [1,3,4,2] => 2
[1,4,2,3] => {{1},{2,4},{3}}
 => [1,4,3,2] => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => [1,4,3,2] => 2
[2,1,3,4] => {{1,2},{3},{4}}
 => [2,1,3,4] => 1
[2,1,4,3] => {{1,2},{3,4}}
 => [2,1,4,3] => 1
[2,3,1,4] => {{1,2,3},{4}}
 => [2,3,1,4] => 2
[2,3,4,1] => {{1,2,3,4}}
 => [2,3,4,1] => 3
[2,4,1,3] => {{1,2,4},{3}}
 => [2,4,3,1] => 3
[2,4,3,1] => {{1,2,4},{3}}
 => [2,4,3,1] => 3
[3,1,2,4] => {{1,3},{2},{4}}
 => [3,2,1,4] => 2
[3,1,4,2] => {{1,3,4},{2}}
 => [3,2,4,1] => 3
[3,2,1,4] => {{1,3},{2},{4}}
 => [3,2,1,4] => 2
[3,2,4,1] => {{1,3,4},{2}}
 => [3,2,4,1] => 3
[3,4,1,2] => {{1,3},{2,4}}
 => [3,4,1,2] => 2
[3,4,2,1] => {{1,3},{2,4}}
 => [3,4,1,2] => 2
[4,1,2,3] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,1,3,2] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,2,1,3] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,2,3,1] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,3,1,2] => {{1,4},{2,3}}
 => [4,3,2,1] => 3
[4,3,2,1] => {{1,4},{2,3}}
 => [4,3,2,1] => 3
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => 0
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => 1
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => 1
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => [1,2,4,5,3] => 2
[1,2,5,3,4] => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => 2
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => 2
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => 1
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => [1,3,2,5,4] => 1
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => [1,3,4,2,5] => 2
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => [1,3,4,5,2] => 3
[1,3,5,2,4] => {{1},{2,3,5},{4}}
 => [1,3,5,4,2] => 3
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => [1,3,5,4,2] => 3
[1,4,2,3,5] => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => 2
[1,4,2,5,3] => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => 3
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => 2
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => [1,4,5,2,3] => 2
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: St000503
(load all 5 compositions to match this statistic)
Mapping
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000503: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => {{1}}
 => ? = 0
[1,2] => {{1},{2}}
 => 0
[2,1] => {{1,2}}
 => 1
[1,2,3] => {{1},{2},{3}}
 => 0
[1,3,2] => {{1},{2,3}}
 => 1
[2,1,3] => {{1,2},{3}}
 => 1
[2,3,1] => {{1,2,3}}
 => 2
[3,1,2] => {{1,3},{2}}
 => 2
[3,2,1] => {{1,3},{2}}
 => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => 0
[1,2,4,3] => {{1},{2},{3,4}}
 => 1
[1,3,2,4] => {{1},{2,3},{4}}
 => 1
[1,3,4,2] => {{1},{2,3,4}}
 => 2
[1,4,2,3] => {{1},{2,4},{3}}
 => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => 2
[2,1,3,4] => {{1,2},{3},{4}}
 => 1
[2,1,4,3] => {{1,2},{3,4}}
 => 1
[2,3,1,4] => {{1,2,3},{4}}
 => 2
[2,3,4,1] => {{1,2,3,4}}
 => 3
[2,4,1,3] => {{1,2,4},{3}}
 => 3
[2,4,3,1] => {{1,2,4},{3}}
 => 3
[3,1,2,4] => {{1,3},{2},{4}}
 => 2
[3,1,4,2] => {{1,3,4},{2}}
 => 3
[3,2,1,4] => {{1,3},{2},{4}}
 => 2
[3,2,4,1] => {{1,3,4},{2}}
 => 3
[3,4,1,2] => {{1,3},{2,4}}
 => 2
[3,4,2,1] => {{1,3},{2,4}}
 => 2
[4,1,2,3] => {{1,4},{2},{3}}
 => 3
[4,1,3,2] => {{1,4},{2},{3}}
 => 3
[4,2,1,3] => {{1,4},{2},{3}}
 => 3
[4,2,3,1] => {{1,4},{2},{3}}
 => 3
[4,3,1,2] => {{1,4},{2,3}}
 => 3
[4,3,2,1] => {{1,4},{2,3}}
 => 3
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => 0
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => 1
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => 1
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => 2
[1,2,5,3,4] => {{1},{2},{3,5},{4}}
 => 2
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => 2
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => 1
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => 1
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => 2
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => 3
[1,3,5,2,4] => {{1},{2,3,5},{4}}
 => 3
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => 3
[1,4,2,3,5] => {{1},{2,4},{3},{5}}
 => 2
[1,4,2,5,3] => {{1},{2,4,5},{3}}
 => 3
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => 2
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => 2
[1,4,5,3,2] => {{1},{2,4},{3,5}}
 => 2
Description
The maximal difference between two elements in a common block.
Matching statistic: St000956
(load all 3 compositions to match this statistic)
Mapping
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
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] => {{1}}
 => [1] => ? = 0
[1,2] => {{1},{2}}
 => [1,2] => 0
[2,1] => {{1,2}}
 => [2,1] => 1
[1,2,3] => {{1},{2},{3}}
 => [1,2,3] => 0
[1,3,2] => {{1},{2,3}}
 => [1,3,2] => 1
[2,1,3] => {{1,2},{3}}
 => [2,1,3] => 1
[2,3,1] => {{1,2,3}}
 => [2,3,1] => 2
[3,1,2] => {{1,3},{2}}
 => [3,2,1] => 2
[3,2,1] => {{1,3},{2}}
 => [3,2,1] => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => [1,2,3,4] => 0
[1,2,4,3] => {{1},{2},{3,4}}
 => [1,2,4,3] => 1
[1,3,2,4] => {{1},{2,3},{4}}
 => [1,3,2,4] => 1
[1,3,4,2] => {{1},{2,3,4}}
 => [1,3,4,2] => 2
[1,4,2,3] => {{1},{2,4},{3}}
 => [1,4,3,2] => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => [1,4,3,2] => 2
[2,1,3,4] => {{1,2},{3},{4}}
 => [2,1,3,4] => 1
[2,1,4,3] => {{1,2},{3,4}}
 => [2,1,4,3] => 1
[2,3,1,4] => {{1,2,3},{4}}
 => [2,3,1,4] => 2
[2,3,4,1] => {{1,2,3,4}}
 => [2,3,4,1] => 3
[2,4,1,3] => {{1,2,4},{3}}
 => [2,4,3,1] => 3
[2,4,3,1] => {{1,2,4},{3}}
 => [2,4,3,1] => 3
[3,1,2,4] => {{1,3},{2},{4}}
 => [3,2,1,4] => 2
[3,1,4,2] => {{1,3,4},{2}}
 => [3,2,4,1] => 3
[3,2,1,4] => {{1,3},{2},{4}}
 => [3,2,1,4] => 2
[3,2,4,1] => {{1,3,4},{2}}
 => [3,2,4,1] => 3
[3,4,1,2] => {{1,3},{2,4}}
 => [3,4,1,2] => 2
[3,4,2,1] => {{1,3},{2,4}}
 => [3,4,1,2] => 2
[4,1,2,3] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,1,3,2] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,2,1,3] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,2,3,1] => {{1,4},{2},{3}}
 => [4,2,3,1] => 3
[4,3,1,2] => {{1,4},{2,3}}
 => [4,3,2,1] => 3
[4,3,2,1] => {{1,4},{2,3}}
 => [4,3,2,1] => 3
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => 0
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => 1
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => 1
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => [1,2,4,5,3] => 2
[1,2,5,3,4] => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => 2
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => 2
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => 1
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => [1,3,2,5,4] => 1
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => [1,3,4,2,5] => 2
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => [1,3,4,5,2] => 3
[1,3,5,2,4] => {{1},{2,3,5},{4}}
 => [1,3,5,4,2] => 3
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => [1,3,5,4,2] => 3
[1,4,2,3,5] => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => 2
[1,4,2,5,3] => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => 3
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => 2
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => [1,4,5,2,3] => 2
[1,4,5,3,2] => {{1},{2,4},{3,5}}
 => [1,4,5,2,3] => 2
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
Mapping
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00080: Set partitions —to permutation⟶ Permutations
Mp00066: Permutations —inverse⟶ Permutations
St000141: Permutations ⟶ ℤResult quality: 74% ●values known / values provided: 74%●distinct values known / distinct values provided: 100%
Values
[1] => {{1}}
 => [1] => [1] => 0
[1,2] => {{1},{2}}
 => [1,2] => [1,2] => 0
[2,1] => {{1,2}}
 => [2,1] => [2,1] => 1
[1,2,3] => {{1},{2},{3}}
 => [1,2,3] => [1,2,3] => 0
[1,3,2] => {{1},{2,3}}
 => [1,3,2] => [1,3,2] => 1
[2,1,3] => {{1,2},{3}}
 => [2,1,3] => [2,1,3] => 1
[2,3,1] => {{1,2,3}}
 => [2,3,1] => [3,1,2] => 2
[3,1,2] => {{1,3},{2}}
 => [3,2,1] => [3,2,1] => 2
[3,2,1] => {{1,3},{2}}
 => [3,2,1] => [3,2,1] => 2
[1,2,3,4] => {{1},{2},{3},{4}}
 => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => {{1},{2},{3,4}}
 => [1,2,4,3] => [1,2,4,3] => 1
[1,3,2,4] => {{1},{2,3},{4}}
 => [1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => {{1},{2,3,4}}
 => [1,3,4,2] => [1,4,2,3] => 2
[1,4,2,3] => {{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => 2
[1,4,3,2] => {{1},{2,4},{3}}
 => [1,4,3,2] => [1,4,3,2] => 2
[2,1,3,4] => {{1,2},{3},{4}}
 => [2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => {{1,2},{3,4}}
 => [2,1,4,3] => [2,1,4,3] => 1
[2,3,1,4] => {{1,2,3},{4}}
 => [2,3,1,4] => [3,1,2,4] => 2
[2,3,4,1] => {{1,2,3,4}}
 => [2,3,4,1] => [4,1,2,3] => 3
[2,4,1,3] => {{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => 3
[2,4,3,1] => {{1,2,4},{3}}
 => [2,4,3,1] => [4,1,3,2] => 3
[3,1,2,4] => {{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => 2
[3,1,4,2] => {{1,3,4},{2}}
 => [3,2,4,1] => [4,2,1,3] => 3
[3,2,1,4] => {{1,3},{2},{4}}
 => [3,2,1,4] => [3,2,1,4] => 2
[3,2,4,1] => {{1,3,4},{2}}
 => [3,2,4,1] => [4,2,1,3] => 3
[3,4,1,2] => {{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => 2
[3,4,2,1] => {{1,3},{2,4}}
 => [3,4,1,2] => [3,4,1,2] => 2
[4,1,2,3] => {{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => 3
[4,1,3,2] => {{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => 3
[4,2,1,3] => {{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => 3
[4,2,3,1] => {{1,4},{2},{3}}
 => [4,2,3,1] => [4,2,3,1] => 3
[4,3,1,2] => {{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => 3
[4,3,2,1] => {{1,4},{2,3}}
 => [4,3,2,1] => [4,3,2,1] => 3
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => [1,2,3,4,5] => [1,2,3,4,5] => 0
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => [1,2,3,5,4] => [1,2,3,5,4] => 1
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => [1,2,4,3,5] => [1,2,4,3,5] => 1
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => [1,2,4,5,3] => [1,2,5,3,4] => 2
[1,2,5,3,4] => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => 2
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => [1,2,5,4,3] => [1,2,5,4,3] => 2
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => [1,3,2,4,5] => [1,3,2,4,5] => 1
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => [1,3,2,5,4] => [1,3,2,5,4] => 1
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => [1,3,4,2,5] => [1,4,2,3,5] => 2
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => [1,3,4,5,2] => [1,5,2,3,4] => 3
[1,3,5,2,4] => {{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,5,2,4,3] => 3
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => [1,3,5,4,2] => [1,5,2,4,3] => 3
[1,4,2,3,5] => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,2,5,3] => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,5,3,2,4] => 3
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => [1,4,3,2,5] => [1,4,3,2,5] => 2
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => [1,4,3,5,2] => [1,5,3,2,4] => 3
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => [1,4,5,2,3] => [1,4,5,2,3] => 2
[1,2,3,4,6,7,5] => {{1},{2},{3},{4},{5,6,7}}
 => [1,2,3,4,6,7,5] => [1,2,3,4,7,5,6] => ? = 2
[1,2,3,4,7,5,6] => {{1},{2},{3},{4},{5,7},{6}}
 => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => ? = 2
[1,2,3,4,7,6,5] => {{1},{2},{3},{4},{5,7},{6}}
 => [1,2,3,4,7,6,5] => [1,2,3,4,7,6,5] => ? = 2
[1,2,3,5,4,6,7] => {{1},{2},{3},{4,5},{6},{7}}
 => [1,2,3,5,4,6,7] => [1,2,3,5,4,6,7] => ? = 1
[1,2,3,5,4,7,6] => {{1},{2},{3},{4,5},{6,7}}
 => [1,2,3,5,4,7,6] => [1,2,3,5,4,7,6] => ? = 1
[1,2,3,5,6,4,7] => {{1},{2},{3},{4,5,6},{7}}
 => [1,2,3,5,6,4,7] => [1,2,3,6,4,5,7] => ? = 2
[1,2,3,5,6,7,4] => {{1},{2},{3},{4,5,6,7}}
 => [1,2,3,5,6,7,4] => [1,2,3,7,4,5,6] => ? = 3
[1,2,3,5,7,4,6] => {{1},{2},{3},{4,5,7},{6}}
 => [1,2,3,5,7,6,4] => [1,2,3,7,4,6,5] => ? = 3
[1,2,3,5,7,6,4] => {{1},{2},{3},{4,5,7},{6}}
 => [1,2,3,5,7,6,4] => [1,2,3,7,4,6,5] => ? = 3
[1,2,3,6,4,5,7] => {{1},{2},{3},{4,6},{5},{7}}
 => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => ? = 2
[1,2,3,6,4,7,5] => {{1},{2},{3},{4,6,7},{5}}
 => [1,2,3,6,5,7,4] => [1,2,3,7,5,4,6] => ? = 3
[1,2,3,6,5,4,7] => {{1},{2},{3},{4,6},{5},{7}}
 => [1,2,3,6,5,4,7] => [1,2,3,6,5,4,7] => ? = 2
[1,2,3,6,5,7,4] => {{1},{2},{3},{4,6,7},{5}}
 => [1,2,3,6,5,7,4] => [1,2,3,7,5,4,6] => ? = 3
[1,2,3,6,7,4,5] => {{1},{2},{3},{4,6},{5,7}}
 => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => ? = 2
[1,2,3,6,7,5,4] => {{1},{2},{3},{4,6},{5,7}}
 => [1,2,3,6,7,4,5] => [1,2,3,6,7,4,5] => ? = 2
[1,2,3,7,4,5,6] => {{1},{2},{3},{4,7},{5},{6}}
 => [1,2,3,7,5,6,4] => [1,2,3,7,5,6,4] => ? = 3
[1,2,3,7,4,6,5] => {{1},{2},{3},{4,7},{5},{6}}
 => [1,2,3,7,5,6,4] => [1,2,3,7,5,6,4] => ? = 3
[1,2,3,7,5,4,6] => {{1},{2},{3},{4,7},{5},{6}}
 => [1,2,3,7,5,6,4] => [1,2,3,7,5,6,4] => ? = 3
[1,2,3,7,5,6,4] => {{1},{2},{3},{4,7},{5},{6}}
 => [1,2,3,7,5,6,4] => [1,2,3,7,5,6,4] => ? = 3
[1,2,3,7,6,4,5] => {{1},{2},{3},{4,7},{5,6}}
 => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3
[1,2,3,7,6,5,4] => {{1},{2},{3},{4,7},{5,6}}
 => [1,2,3,7,6,5,4] => [1,2,3,7,6,5,4] => ? = 3
[1,2,4,3,5,6,7] => {{1},{2},{3,4},{5},{6},{7}}
 => [1,2,4,3,5,6,7] => [1,2,4,3,5,6,7] => ? = 1
[1,2,4,3,5,7,6] => {{1},{2},{3,4},{5},{6,7}}
 => [1,2,4,3,5,7,6] => [1,2,4,3,5,7,6] => ? = 1
[1,2,4,3,6,5,7] => {{1},{2},{3,4},{5,6},{7}}
 => [1,2,4,3,6,5,7] => [1,2,4,3,6,5,7] => ? = 1
[1,2,4,3,6,7,5] => {{1},{2},{3,4},{5,6,7}}
 => [1,2,4,3,6,7,5] => [1,2,4,3,7,5,6] => ? = 2
[1,2,4,3,7,5,6] => {{1},{2},{3,4},{5,7},{6}}
 => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => ? = 2
[1,2,4,3,7,6,5] => {{1},{2},{3,4},{5,7},{6}}
 => [1,2,4,3,7,6,5] => [1,2,4,3,7,6,5] => ? = 2
[1,2,4,5,3,6,7] => {{1},{2},{3,4,5},{6},{7}}
 => [1,2,4,5,3,6,7] => [1,2,5,3,4,6,7] => ? = 2
[1,2,4,5,3,7,6] => {{1},{2},{3,4,5},{6,7}}
 => [1,2,4,5,3,7,6] => [1,2,5,3,4,7,6] => ? = 2
[1,2,4,5,6,3,7] => {{1},{2},{3,4,5,6},{7}}
 => [1,2,4,5,6,3,7] => [1,2,6,3,4,5,7] => ? = 3
[1,2,4,5,6,7,3] => {{1},{2},{3,4,5,6,7}}
 => [1,2,4,5,6,7,3] => [1,2,7,3,4,5,6] => ? = 4
[1,2,4,5,7,3,6] => {{1},{2},{3,4,5,7},{6}}
 => [1,2,4,5,7,6,3] => [1,2,7,3,4,6,5] => ? = 4
[1,2,4,5,7,6,3] => {{1},{2},{3,4,5,7},{6}}
 => [1,2,4,5,7,6,3] => [1,2,7,3,4,6,5] => ? = 4
[1,2,4,6,3,5,7] => {{1},{2},{3,4,6},{5},{7}}
 => [1,2,4,6,5,3,7] => [1,2,6,3,5,4,7] => ? = 3
[1,2,4,6,3,7,5] => {{1},{2},{3,4,6,7},{5}}
 => [1,2,4,6,5,7,3] => [1,2,7,3,5,4,6] => ? = 4
[1,2,4,6,5,3,7] => {{1},{2},{3,4,6},{5},{7}}
 => [1,2,4,6,5,3,7] => [1,2,6,3,5,4,7] => ? = 3
[1,2,4,6,5,7,3] => {{1},{2},{3,4,6,7},{5}}
 => [1,2,4,6,5,7,3] => [1,2,7,3,5,4,6] => ? = 4
[1,2,4,6,7,3,5] => {{1},{2},{3,4,6},{5,7}}
 => [1,2,4,6,7,3,5] => [1,2,6,3,7,4,5] => ? = 3
[1,2,4,6,7,5,3] => {{1},{2},{3,4,6},{5,7}}
 => [1,2,4,6,7,3,5] => [1,2,6,3,7,4,5] => ? = 3
[1,2,4,7,3,5,6] => {{1},{2},{3,4,7},{5},{6}}
 => [1,2,4,7,5,6,3] => [1,2,7,3,5,6,4] => ? = 4
[1,2,4,7,3,6,5] => {{1},{2},{3,4,7},{5},{6}}
 => [1,2,4,7,5,6,3] => [1,2,7,3,5,6,4] => ? = 4
[1,2,4,7,5,3,6] => {{1},{2},{3,4,7},{5},{6}}
 => [1,2,4,7,5,6,3] => [1,2,7,3,5,6,4] => ? = 4
[1,2,4,7,5,6,3] => {{1},{2},{3,4,7},{5},{6}}
 => [1,2,4,7,5,6,3] => [1,2,7,3,5,6,4] => ? = 4
[1,2,4,7,6,3,5] => {{1},{2},{3,4,7},{5,6}}
 => [1,2,4,7,6,5,3] => [1,2,7,3,6,5,4] => ? = 4
[1,2,4,7,6,5,3] => {{1},{2},{3,4,7},{5,6}}
 => [1,2,4,7,6,5,3] => [1,2,7,3,6,5,4] => ? = 4
[1,2,5,3,4,6,7] => {{1},{2},{3,5},{4},{6},{7}}
 => [1,2,5,4,3,6,7] => [1,2,5,4,3,6,7] => ? = 2
[1,2,5,3,4,7,6] => {{1},{2},{3,5},{4},{6,7}}
 => [1,2,5,4,3,7,6] => [1,2,5,4,3,7,6] => ? = 2
[1,2,5,3,6,4,7] => {{1},{2},{3,5,6},{4},{7}}
 => [1,2,5,4,6,3,7] => [1,2,6,4,3,5,7] => ? = 3
[1,2,5,3,6,7,4] => {{1},{2},{3,5,6,7},{4}}
 => [1,2,5,4,6,7,3] => [1,2,7,4,3,5,6] => ? = 4
[1,2,5,3,7,4,6] => {{1},{2},{3,5,7},{4},{6}}
 => [1,2,5,4,7,6,3] => [1,2,7,4,3,6,5] => ? = 4
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: St001232
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
Mp00222: Dyck paths —peaks-to-valleys⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 100%
Values
[1] => [1,0]
 => [1,1,0,0]
 => [1,0,1,0]
 => 1 = 0 + 1
[1,2] => [1,0,1,0]
 => [1,1,0,1,0,0]
 => [1,0,1,0,1,0]
 => ? = 0 + 1
[2,1] => [1,1,0,0]
 => [1,1,1,0,0,0]
 => [1,1,0,1,0,0]
 => 2 = 1 + 1
[1,2,3] => [1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0]
 => ? = 0 + 1
[1,3,2] => [1,0,1,1,0,0]
 => [1,1,0,1,1,0,0,0]
 => [1,0,1,1,0,1,0,0]
 => ? = 1 + 1
[2,1,3] => [1,1,0,0,1,0]
 => [1,1,1,0,0,1,0,0]
 => [1,1,0,1,0,0,1,0]
 => ? = 1 + 1
[2,3,1] => [1,1,0,1,0,0]
 => [1,1,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,0]
 => ? = 2 + 1
[3,1,2] => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 2 + 1
[3,2,1] => [1,1,1,0,0,0]
 => [1,1,1,1,0,0,0,0]
 => [1,1,1,0,1,0,0,0]
 => 3 = 2 + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0]
 => ? = 1 + 1
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,0]
 => ? = 2 + 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [1,1,0,1,1,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [1,1,1,0,0,1,1,0,0,0]
 => [1,1,0,1,1,0,0,1,0,0]
 => ? = 1 + 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => [1,1,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => [1,1,0,1,0,1,0,1,0,0]
 => ? = 3 + 1
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 3 + 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [1,1,1,0,1,1,0,0,0,0]
 => [1,1,0,1,1,0,1,0,0,0]
 => ? = 3 + 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3 + 1
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [1,1,1,1,0,0,0,1,0,0]
 => [1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [1,1,1,1,0,0,1,0,0,0]
 => [1,1,1,0,1,0,0,1,0,0]
 => ? = 3 + 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 2 + 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => [1,1,1,0,1,0,1,0,0,0]
 => ? = 2 + 1
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,1,3,2] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,0,1,0,0,0,0]
 => 4 = 3 + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [1,1,0,1,0,1,0,1,0,1,0,0]
 => [1,0,1,0,1,0,1,0,1,0,1,0]
 => ? = 0 + 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,0,1,0,1,0,1,1,0,0,0]
 => [1,0,1,0,1,0,1,1,0,1,0,0]
 => ? = 1 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,0,1,0,1,1,0,0,1,0,0]
 => [1,0,1,0,1,1,0,1,0,0,1,0]
 => ? = 1 + 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,0,1,0,1,1,0,1,0,0,0]
 => [1,0,1,0,1,1,0,1,0,1,0,0]
 => ? = 2 + 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,0,1,0,1,1,1,0,0,0,0]
 => [1,0,1,0,1,1,1,0,1,0,0,0]
 => ? = 2 + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [1,1,0,1,1,0,0,1,0,1,0,0]
 => [1,0,1,1,0,1,0,0,1,0,1,0]
 => ? = 1 + 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [1,1,0,1,1,0,0,1,1,0,0,0]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => ? = 1 + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [1,1,0,1,1,0,1,0,0,1,0,0]
 => [1,0,1,1,0,1,0,1,0,0,1,0]
 => ? = 2 + 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [1,1,0,1,1,0,1,0,1,0,0,0]
 => [1,0,1,1,0,1,0,1,0,1,0,0]
 => ? = 3 + 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => ? = 3 + 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [1,1,0,1,1,0,1,1,0,0,0,0]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => ? = 3 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => ? = 3 + 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [1,1,0,1,1,1,0,0,0,1,0,0]
 => [1,0,1,1,1,0,1,0,0,0,1,0]
 => ? = 2 + 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [1,1,0,1,1,1,0,0,1,0,0,0]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => ? = 3 + 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => ? = 2 + 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [1,1,0,1,1,1,0,1,0,0,0,0]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => ? = 2 + 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [1,1,0,1,1,1,1,0,0,0,0,0]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => ? = 3 + 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [1,1,1,0,0,1,0,1,0,1,0,0]
 => [1,1,0,1,0,0,1,0,1,0,1,0]
 => ? = 1 + 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [1,1,1,0,0,1,0,1,1,0,0,0]
 => [1,1,0,1,0,0,1,1,0,1,0,0]
 => ? = 1 + 1
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0]
 => [1,1,1,0,0,1,1,0,0,1,0,0]
 => [1,1,0,1,1,0,0,1,0,0,1,0]
 => ? = 1 + 1
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,0,1,0,0,0,0,0]
 => 5 = 4 + 1
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => 6 = 5 + 1
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001879
(load all 2 compositions to match this statistic)
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00047: Ordered trees —to poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 83%
Values
[1] => [1,0]
 => [[]]
 => ([(0,1)],2)
 => ? = 0 + 1
[1,2] => [1,0,1,0]
 => [[],[]]
 => ([(0,2),(1,2)],3)
 => ? = 0 + 1
[2,1] => [1,1,0,0]
 => [[[]]]
 => ([(0,2),(2,1)],3)
 => 2 = 1 + 1
[1,2,3] => [1,0,1,0,1,0]
 => [[],[],[]]
 => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 1
[1,3,2] => [1,0,1,1,0,0]
 => [[],[[]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[2,1,3] => [1,1,0,0,1,0]
 => [[[]],[]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 1
[2,3,1] => [1,1,0,1,0,0]
 => [[[],[]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 1
[3,1,2] => [1,1,1,0,0,0]
 => [[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 2 + 1
[3,2,1] => [1,1,1,0,0,0]
 => [[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 3 = 2 + 1
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [[],[],[],[]]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 0 + 1
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [[],[],[[]]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 1
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [[],[[]],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 1
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [[],[[],[]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [[[]],[],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 1
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [[[]],[[]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 1
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [[[],[]],[]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 2 + 1
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [[[],[],[]]]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ? = 3 + 1
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 1
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 1
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [[[[],[]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2 + 1
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [[[[],[]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2 + 1
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,1,3,2] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 4 = 3 + 1
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 1
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [[],[],[],[[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [[],[],[[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [[],[],[[],[]]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 + 1
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 1
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 1
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [[],[[]],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [[],[[]],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1 + 1
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [[],[[],[]],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 + 1
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [[],[[],[],[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 3 + 1
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 1
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 1
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 1
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 1
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 1
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 1
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [[],[[[],[]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 2 + 1
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [[],[[[],[]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 2 + 1
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 1
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [[[]],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 1
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [[[]],[],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1 + 1
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 5 = 4 + 1
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 1
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 6 = 5 + 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: St001880
(load all 2 compositions to match this statistic)
Mapping
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00026: Dyck paths —to ordered tree⟶ Ordered trees
Mp00047: Ordered trees —to poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 83%
Values
[1] => [1,0]
 => [[]]
 => ([(0,1)],2)
 => ? = 0 + 2
[1,2] => [1,0,1,0]
 => [[],[]]
 => ([(0,2),(1,2)],3)
 => ? = 0 + 2
[2,1] => [1,1,0,0]
 => [[[]]]
 => ([(0,2),(2,1)],3)
 => 3 = 1 + 2
[1,2,3] => [1,0,1,0,1,0]
 => [[],[],[]]
 => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 2
[1,3,2] => [1,0,1,1,0,0]
 => [[],[[]]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 2
[2,1,3] => [1,1,0,0,1,0]
 => [[[]],[]]
 => ([(0,3),(1,2),(2,3)],4)
 => ? = 1 + 2
[2,3,1] => [1,1,0,1,0,0]
 => [[[],[]]]
 => ([(0,3),(1,3),(3,2)],4)
 => ? = 2 + 2
[3,1,2] => [1,1,1,0,0,0]
 => [[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 2 + 2
[3,2,1] => [1,1,1,0,0,0]
 => [[[[]]]]
 => ([(0,3),(2,1),(3,2)],4)
 => 4 = 2 + 2
[1,2,3,4] => [1,0,1,0,1,0,1,0]
 => [[],[],[],[]]
 => ([(0,4),(1,4),(2,4),(3,4)],5)
 => ? = 0 + 2
[1,2,4,3] => [1,0,1,0,1,1,0,0]
 => [[],[],[[]]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 2
[1,3,2,4] => [1,0,1,1,0,0,1,0]
 => [[],[[]],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 2
[1,3,4,2] => [1,0,1,1,0,1,0,0]
 => [[],[[],[]]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 2 + 2
[1,4,2,3] => [1,0,1,1,1,0,0,0]
 => [[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[1,4,3,2] => [1,0,1,1,1,0,0,0]
 => [[],[[[]]]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[2,1,3,4] => [1,1,0,0,1,0,1,0]
 => [[[]],[],[]]
 => ([(0,4),(1,4),(2,3),(3,4)],5)
 => ? = 1 + 2
[2,1,4,3] => [1,1,0,0,1,1,0,0]
 => [[[]],[[]]]
 => ([(0,3),(1,2),(2,4),(3,4)],5)
 => ? = 1 + 2
[2,3,1,4] => [1,1,0,1,0,0,1,0]
 => [[[],[]],[]]
 => ([(0,4),(1,3),(2,3),(3,4)],5)
 => ? = 2 + 2
[2,3,4,1] => [1,1,0,1,0,1,0,0]
 => [[[],[],[]]]
 => ([(0,4),(1,4),(2,4),(4,3)],5)
 => ? = 3 + 2
[2,4,1,3] => [1,1,0,1,1,0,0,0]
 => [[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 2
[2,4,3,1] => [1,1,0,1,1,0,0,0]
 => [[[],[[]]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 2
[3,1,2,4] => [1,1,1,0,0,0,1,0]
 => [[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[3,1,4,2] => [1,1,1,0,0,1,0,0]
 => [[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 2
[3,2,1,4] => [1,1,1,0,0,0,1,0]
 => [[[[]]],[]]
 => ([(0,4),(1,2),(2,3),(3,4)],5)
 => ? = 2 + 2
[3,2,4,1] => [1,1,1,0,0,1,0,0]
 => [[[[]],[]]]
 => ([(0,4),(1,2),(2,4),(4,3)],5)
 => ? = 3 + 2
[3,4,1,2] => [1,1,1,0,1,0,0,0]
 => [[[[],[]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2 + 2
[3,4,2,1] => [1,1,1,0,1,0,0,0]
 => [[[[],[]]]]
 => ([(0,4),(1,4),(2,3),(4,2)],5)
 => ? = 2 + 2
[4,1,2,3] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,1,3,2] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,2,1,3] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,2,3,1] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,3,1,2] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[4,3,2,1] => [1,1,1,1,0,0,0,0]
 => [[[[[]]]]]
 => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 5 = 3 + 2
[1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0]
 => [[],[],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? = 0 + 2
[1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0]
 => [[],[],[],[[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 2
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0]
 => [[],[],[[]],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 2
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0]
 => [[],[],[[],[]]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 + 2
[1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0]
 => [[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 2
[1,2,5,4,3] => [1,0,1,0,1,1,1,0,0,0]
 => [[],[],[[[]]]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 2
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0]
 => [[],[[]],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 2
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0]
 => [[],[[]],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1 + 2
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0]
 => [[],[[],[]],[]]
 => ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
 => ? = 2 + 2
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0]
 => [[],[[],[],[]]]
 => ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
 => ? = 3 + 2
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0]
 => [[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 2
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0]
 => [[],[[],[[]]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 2
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0]
 => [[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 2
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0]
 => [[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 2
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0]
 => [[],[[[]]],[]]
 => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)
 => ? = 2 + 2
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0]
 => [[],[[[]],[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(5,4)],6)
 => ? = 3 + 2
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0]
 => [[],[[[],[]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 2 + 2
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0]
 => [[],[[[],[]]]]
 => ([(0,5),(1,4),(2,4),(3,5),(4,3)],6)
 => ? = 2 + 2
[1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[1,5,2,4,3] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[1,5,3,2,4] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[1,5,3,4,2] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[1,5,4,2,3] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[1,5,4,3,2] => [1,0,1,1,1,1,0,0,0,0]
 => [[],[[[[]]]]]
 => ([(0,5),(1,4),(2,5),(3,2),(4,3)],6)
 => ? = 3 + 2
[2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0]
 => [[[]],[],[],[]]
 => ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)
 => ? = 1 + 2
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0]
 => [[[]],[],[[]]]
 => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
 => ? = 1 + 2
[5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,2,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,3,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,3,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,1,4,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,2,1,3,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,2,1,4,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,2,3,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,2,3,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,2,4,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,2,4,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,3,1,4,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,3,2,1,4] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,3,2,4,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,3,4,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,1,3,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,2,1,3] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,2,3,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,3,1,2] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[5,4,3,2,1] => [1,1,1,1,1,0,0,0,0,0]
 => [[[[[[]]]]]]
 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
 => 6 = 4 + 2
[6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,3,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,4,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,4,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,2,5,4,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,3,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,3,2,5,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,3,4,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,3,4,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,3,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,3,5,4,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,4,2,5,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,4,3,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,4,3,5,2] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
[6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0]
 => [[[[[[[]]]]]]]
 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
 => 7 = 5 + 2
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001207
(load all 5 compositions to match this statistic)
Mapping
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00238: Permutations —Clarke-Steingrimsson-Zeng⟶ Permutations
Mp00087: Permutations —inverse first fundamental transformation⟶ Permutations
St001207: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 67%
Values
[1] => [1] => [1] => [1] => ? = 0
[1,2] => [1,2] => [1,2] => [1,2] => 0
[2,1] => [2,1] => [2,1] => [2,1] => 1
[1,2,3] => [1,2,3] => [1,2,3] => [1,2,3] => 0
[1,3,2] => [1,3,2] => [1,3,2] => [1,3,2] => 1
[2,1,3] => [2,1,3] => [2,1,3] => [2,1,3] => 1
[2,3,1] => [3,2,1] => [2,3,1] => [3,1,2] => 2
[3,1,2] => [2,3,1] => [3,2,1] => [2,3,1] => 2
[3,2,1] => [3,1,2] => [3,1,2] => [3,2,1] => 2
[1,2,3,4] => [1,2,3,4] => [1,2,3,4] => [1,2,3,4] => 0
[1,2,4,3] => [1,2,4,3] => [1,2,4,3] => [1,2,4,3] => 1
[1,3,2,4] => [1,3,2,4] => [1,3,2,4] => [1,3,2,4] => 1
[1,3,4,2] => [1,4,3,2] => [1,3,4,2] => [1,4,2,3] => 2
[1,4,2,3] => [1,3,4,2] => [1,4,3,2] => [1,3,4,2] => 2
[1,4,3,2] => [1,4,2,3] => [1,4,2,3] => [1,4,3,2] => 2
[2,1,3,4] => [2,1,3,4] => [2,1,3,4] => [2,1,3,4] => 1
[2,1,4,3] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 1
[2,3,1,4] => [3,2,1,4] => [2,3,1,4] => [3,1,2,4] => 2
[2,3,4,1] => [4,2,3,1] => [3,4,2,1] => [4,1,3,2] => 3
[2,4,1,3] => [3,2,4,1] => [4,3,2,1] => [3,2,4,1] => 3
[2,4,3,1] => [4,2,1,3] => [2,4,1,3] => [4,3,1,2] => 3
[3,1,2,4] => [2,3,1,4] => [3,2,1,4] => [2,3,1,4] => 2
[3,1,4,2] => [3,4,1,2] => [4,1,3,2] => [3,4,2,1] => 3
[3,2,1,4] => [3,1,2,4] => [3,1,2,4] => [3,2,1,4] => 2
[3,2,4,1] => [4,3,2,1] => [2,3,4,1] => [4,1,2,3] => 3
[3,4,1,2] => [2,4,3,1] => [3,2,4,1] => [2,4,1,3] => 2
[3,4,2,1] => [4,1,3,2] => [3,4,1,2] => [3,1,4,2] => 2
[4,1,2,3] => [2,3,4,1] => [4,2,3,1] => [2,3,4,1] => 3
[4,1,3,2] => [3,4,2,1] => [2,4,3,1] => [3,4,1,2] => 3
[4,2,1,3] => [3,1,4,2] => [4,3,1,2] => [4,2,3,1] => 3
[4,2,3,1] => [4,3,1,2] => [3,1,4,2] => [4,2,1,3] => 3
[4,3,1,2] => [2,4,1,3] => [4,2,1,3] => [2,4,3,1] => 3
[4,3,2,1] => [4,1,2,3] => [4,1,2,3] => [4,3,2,1] => 3
[1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => [1,2,3,4,5] => ? = 0
[1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => [1,2,3,5,4] => ? = 1
[1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => [1,2,4,3,5] => ? = 1
[1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => [1,2,5,3,4] => ? = 2
[1,2,5,3,4] => [1,2,4,5,3] => [1,2,5,4,3] => [1,2,4,5,3] => ? = 2
[1,2,5,4,3] => [1,2,5,3,4] => [1,2,5,3,4] => [1,2,5,4,3] => ? = 2
[1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => [1,3,2,4,5] => ? = 1
[1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => [1,3,2,5,4] => ? = 1
[1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => [1,4,2,3,5] => ? = 2
[1,3,4,5,2] => [1,5,3,4,2] => [1,4,5,3,2] => [1,5,2,4,3] => ? = 3
[1,3,5,2,4] => [1,4,3,5,2] => [1,5,4,3,2] => [1,4,3,5,2] => ? = 3
[1,3,5,4,2] => [1,5,3,2,4] => [1,3,5,2,4] => [1,5,4,2,3] => ? = 3
[1,4,2,3,5] => [1,3,4,2,5] => [1,4,3,2,5] => [1,3,4,2,5] => ? = 2
[1,4,2,5,3] => [1,4,5,2,3] => [1,5,2,4,3] => [1,4,5,3,2] => ? = 3
[1,4,3,2,5] => [1,4,2,3,5] => [1,4,2,3,5] => [1,4,3,2,5] => ? = 2
[1,4,3,5,2] => [1,5,4,3,2] => [1,3,4,5,2] => [1,5,2,3,4] => ? = 3
[1,4,5,2,3] => [1,3,5,4,2] => [1,4,3,5,2] => [1,3,5,2,4] => ? = 2
[1,4,5,3,2] => [1,5,2,4,3] => [1,4,5,2,3] => [1,4,2,5,3] => ? = 2
[1,5,2,3,4] => [1,3,4,5,2] => [1,5,3,4,2] => [1,3,4,5,2] => ? = 3
[1,5,2,4,3] => [1,4,5,3,2] => [1,3,5,4,2] => [1,4,5,2,3] => ? = 3
[1,5,3,2,4] => [1,4,2,5,3] => [1,5,4,2,3] => [1,5,3,4,2] => ? = 3
[1,5,3,4,2] => [1,5,4,2,3] => [1,4,2,5,3] => [1,5,3,2,4] => ? = 3
[1,5,4,2,3] => [1,3,5,2,4] => [1,5,3,2,4] => [1,3,5,4,2] => ? = 3
[1,5,4,3,2] => [1,5,2,3,4] => [1,5,2,3,4] => [1,5,4,3,2] => ? = 3
[2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => [2,1,3,4,5] => ? = 1
[2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => [2,1,3,5,4] => ? = 1
[2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => [2,1,4,3,5] => ? = 1
[2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,5,3] => [2,1,5,3,4] => ? = 2
[2,1,5,3,4] => [2,1,4,5,3] => [2,1,5,4,3] => [2,1,4,5,3] => ? = 2
[2,1,5,4,3] => [2,1,5,3,4] => [2,1,5,3,4] => [2,1,5,4,3] => ? = 2
[2,3,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => [3,1,2,4,5] => ? = 2
[2,3,1,5,4] => [3,2,1,5,4] => [2,3,1,5,4] => [3,1,2,5,4] => ? = 2
[2,3,4,1,5] => [4,2,3,1,5] => [3,4,2,1,5] => [4,1,3,2,5] => ? = 3
[2,3,4,5,1] => [5,2,3,4,1] => [4,5,2,3,1] => [5,1,4,3,2] => ? = 4
[2,3,5,1,4] => [4,2,3,5,1] => [5,4,2,3,1] => [4,3,2,5,1] => ? = 4
[2,3,5,4,1] => [5,2,3,1,4] => [3,5,2,1,4] => [5,4,1,3,2] => ? = 4
[2,4,1,3,5] => [3,2,4,1,5] => [4,3,2,1,5] => [3,2,4,1,5] => ? = 3
[2,4,1,5,3] => [4,2,5,1,3] => [5,4,2,1,3] => [5,3,2,4,1] => ? = 4
[2,4,3,1,5] => [4,2,1,3,5] => [2,4,1,3,5] => [4,3,1,2,5] => ? = 3
[2,4,3,5,1] => [5,2,4,3,1] => [3,4,5,2,1] => [4,2,5,1,3] => ? = 4
[2,4,5,1,3] => [3,2,5,4,1] => [4,3,2,5,1] => [3,2,5,1,4] => ? = 3
[2,4,5,3,1] => [5,2,1,4,3] => [2,4,5,1,3] => [4,1,2,5,3] => ? = 3
[2,5,1,3,4] => [3,2,4,5,1] => [5,3,2,4,1] => [3,2,4,5,1] => ? = 4
[2,5,1,4,3] => [4,2,5,3,1] => [3,5,4,2,1] => [5,1,3,4,2] => ? = 4
[2,5,3,1,4] => [4,2,1,5,3] => [2,5,4,1,3] => [5,3,4,1,2] => ? = 4
[2,5,3,4,1] => [5,2,4,1,3] => [4,5,2,1,3] => [4,1,5,3,2] => ? = 4
[2,5,4,1,3] => [3,2,5,1,4] => [5,3,2,1,4] => [3,2,5,4,1] => ? = 4
[2,5,4,3,1] => [5,2,1,3,4] => [2,5,1,3,4] => [5,4,3,1,2] => ? = 4
[3,1,2,4,5] => [2,3,1,4,5] => [3,2,1,4,5] => [2,3,1,4,5] => ? = 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 $K[x]/(x^n)$.