Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001497
(load all 17 compositions to match this statistic)
Mapping
St001497: Permutations ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,2] => 2
[2,1] => 1
[1,2,3] => 3
[1,3,2] => 2
[2,1,3] => 3
[2,3,1] => 2
[3,1,2] => 1
[3,2,1] => 2
[1,2,3,4] => 4
[1,2,4,3] => 3
[1,3,2,4] => 4
[1,3,4,2] => 3
[1,4,2,3] => 2
[1,4,3,2] => 3
[2,1,3,4] => 4
[2,1,4,3] => 3
[2,3,1,4] => 4
[2,3,4,1] => 3
[2,4,1,3] => 2
[2,4,3,1] => 3
[3,1,2,4] => 4
[3,1,4,2] => 3
[3,2,1,4] => 4
[3,2,4,1] => 3
[3,4,1,2] => 2
[3,4,2,1] => 2
[4,1,2,3] => 1
[4,1,3,2] => 3
[4,2,1,3] => 2
[4,2,3,1] => 3
[4,3,1,2] => 2
[4,3,2,1] => 2
[1,2,3,4,5] => 5
[1,2,3,5,4] => 4
[1,2,4,3,5] => 5
[1,2,4,5,3] => 4
[1,2,5,3,4] => 3
[1,2,5,4,3] => 4
[1,3,2,4,5] => 5
[1,3,2,5,4] => 4
[1,3,4,2,5] => 5
[1,3,4,5,2] => 4
[1,3,5,2,4] => 3
[1,3,5,4,2] => 4
[1,4,2,3,5] => 5
[1,4,2,5,3] => 4
[1,4,3,2,5] => 5
[1,4,3,5,2] => 4
[1,4,5,2,3] => 3
Description
The position of the largest weak excedence of a permutation.
Matching statistic: St000839
(load all 12 compositions to match this statistic)
Mapping
Mp00066: Permutations —inverse⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000839: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1] => {{1}}
 => 1
[1,2] => [1,2] => {{1},{2}}
 => 2
[2,1] => [2,1] => {{1,2}}
 => 1
[1,2,3] => [1,2,3] => {{1},{2},{3}}
 => 3
[1,3,2] => [1,3,2] => {{1},{2,3}}
 => 2
[2,1,3] => [2,1,3] => {{1,2},{3}}
 => 3
[2,3,1] => [3,1,2] => {{1,3},{2}}
 => 2
[3,1,2] => [2,3,1] => {{1,2,3}}
 => 1
[3,2,1] => [3,2,1] => {{1,3},{2}}
 => 2
[1,2,3,4] => [1,2,3,4] => {{1},{2},{3},{4}}
 => 4
[1,2,4,3] => [1,2,4,3] => {{1},{2},{3,4}}
 => 3
[1,3,2,4] => [1,3,2,4] => {{1},{2,3},{4}}
 => 4
[1,3,4,2] => [1,4,2,3] => {{1},{2,4},{3}}
 => 3
[1,4,2,3] => [1,3,4,2] => {{1},{2,3,4}}
 => 2
[1,4,3,2] => [1,4,3,2] => {{1},{2,4},{3}}
 => 3
[2,1,3,4] => [2,1,3,4] => {{1,2},{3},{4}}
 => 4
[2,1,4,3] => [2,1,4,3] => {{1,2},{3,4}}
 => 3
[2,3,1,4] => [3,1,2,4] => {{1,3},{2},{4}}
 => 4
[2,3,4,1] => [4,1,2,3] => {{1,4},{2},{3}}
 => 3
[2,4,1,3] => [3,1,4,2] => {{1,3,4},{2}}
 => 2
[2,4,3,1] => [4,1,3,2] => {{1,4},{2},{3}}
 => 3
[3,1,2,4] => [2,3,1,4] => {{1,2,3},{4}}
 => 4
[3,1,4,2] => [2,4,1,3] => {{1,2,4},{3}}
 => 3
[3,2,1,4] => [3,2,1,4] => {{1,3},{2},{4}}
 => 4
[3,2,4,1] => [4,2,1,3] => {{1,4},{2},{3}}
 => 3
[3,4,1,2] => [3,4,1,2] => {{1,3},{2,4}}
 => 2
[3,4,2,1] => [4,3,1,2] => {{1,4},{2,3}}
 => 2
[4,1,2,3] => [2,3,4,1] => {{1,2,3,4}}
 => 1
[4,1,3,2] => [2,4,3,1] => {{1,2,4},{3}}
 => 3
[4,2,1,3] => [3,2,4,1] => {{1,3,4},{2}}
 => 2
[4,2,3,1] => [4,2,3,1] => {{1,4},{2},{3}}
 => 3
[4,3,1,2] => [3,4,2,1] => {{1,3},{2,4}}
 => 2
[4,3,2,1] => [4,3,2,1] => {{1,4},{2,3}}
 => 2
[1,2,3,4,5] => [1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => 5
[1,2,3,5,4] => [1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => 4
[1,2,4,3,5] => [1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => 5
[1,2,4,5,3] => [1,2,5,3,4] => {{1},{2},{3,5},{4}}
 => 4
[1,2,5,3,4] => [1,2,4,5,3] => {{1},{2},{3,4,5}}
 => 3
[1,2,5,4,3] => [1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => 4
[1,3,2,4,5] => [1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => 5
[1,3,2,5,4] => [1,3,2,5,4] => {{1},{2,3},{4,5}}
 => 4
[1,3,4,2,5] => [1,4,2,3,5] => {{1},{2,4},{3},{5}}
 => 5
[1,3,4,5,2] => [1,5,2,3,4] => {{1},{2,5},{3},{4}}
 => 4
[1,3,5,2,4] => [1,4,2,5,3] => {{1},{2,4,5},{3}}
 => 3
[1,3,5,4,2] => [1,5,2,4,3] => {{1},{2,5},{3},{4}}
 => 4
[1,4,2,3,5] => [1,3,4,2,5] => {{1},{2,3,4},{5}}
 => 5
[1,4,2,5,3] => [1,3,5,2,4] => {{1},{2,3,5},{4}}
 => 4
[1,4,3,2,5] => [1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => 5
[1,4,3,5,2] => [1,5,3,2,4] => {{1},{2,5},{3},{4}}
 => 4
[1,4,5,2,3] => [1,4,5,2,3] => {{1},{2,4},{3,5}}
 => 3
Description
The largest opener of a set partition. An opener (or left hand endpoint) of a set partition is a number that is minimal in its block. For this statistic, singletons are considered as openers.