- FindStat

Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St000577
(load all 3 compositions to match this statistic)

Mapping

Mp00240: Permutations —weak exceedance partition⟶ Set partitions
St000577: Set partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1,2] => {{1},{2}}
 => 1
[2,1] => {{1,2}}
 => 0
[1,2,3] => {{1},{2},{3}}
 => 3
[1,3,2] => {{1},{2,3}}
 => 2
[2,1,3] => {{1,2},{3}}
 => 1
[2,3,1] => {{1,2,3}}
 => 0
[3,1,2] => {{1,3},{2}}
 => 1
[3,2,1] => {{1,3},{2}}
 => 1
[1,2,3,4] => {{1},{2},{3},{4}}
 => 6
[1,2,4,3] => {{1},{2},{3,4}}
 => 5
[1,3,2,4] => {{1},{2,3},{4}}
 => 4
[1,3,4,2] => {{1},{2,3,4}}
 => 3
[1,4,2,3] => {{1},{2,4},{3}}
 => 4
[1,4,3,2] => {{1},{2,4},{3}}
 => 4
[2,1,3,4] => {{1,2},{3},{4}}
 => 3
[2,1,4,3] => {{1,2},{3,4}}
 => 2
[2,3,1,4] => {{1,2,3},{4}}
 => 1
[2,3,4,1] => {{1,2,3,4}}
 => 0
[2,4,1,3] => {{1,2,4},{3}}
 => 1
[2,4,3,1] => {{1,2,4},{3}}
 => 1
[3,1,2,4] => {{1,3},{2},{4}}
 => 3
[3,1,4,2] => {{1,3,4},{2}}
 => 2
[3,2,1,4] => {{1,3},{2},{4}}
 => 3
[3,2,4,1] => {{1,3,4},{2}}
 => 2
[3,4,1,2] => {{1,3},{2,4}}
 => 1
[3,4,2,1] => {{1,3},{2,4}}
 => 1
[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}}
 => 1
[4,3,2,1] => {{1,4},{2,3}}
 => 1
[1,2,3,4,5] => {{1},{2},{3},{4},{5}}
 => 10
[1,2,3,5,4] => {{1},{2},{3},{4,5}}
 => 9
[1,2,4,3,5] => {{1},{2},{3,4},{5}}
 => 8
[1,2,4,5,3] => {{1},{2},{3,4,5}}
 => 7
[1,2,5,3,4] => {{1},{2},{3,5},{4}}
 => 8
[1,2,5,4,3] => {{1},{2},{3,5},{4}}
 => 8
[1,3,2,4,5] => {{1},{2,3},{4},{5}}
 => 7
[1,3,2,5,4] => {{1},{2,3},{4,5}}
 => 6
[1,3,4,2,5] => {{1},{2,3,4},{5}}
 => 5
[1,3,4,5,2] => {{1},{2,3,4,5}}
 => 4
[1,3,5,2,4] => {{1},{2,3,5},{4}}
 => 5
[1,3,5,4,2] => {{1},{2,3,5},{4}}
 => 5
[1,4,2,3,5] => {{1},{2,4},{3},{5}}
 => 7
[1,4,2,5,3] => {{1},{2,4,5},{3}}
 => 6
[1,4,3,2,5] => {{1},{2,4},{3},{5}}
 => 7
[1,4,3,5,2] => {{1},{2,4,5},{3}}
 => 6
[1,4,5,2,3] => {{1},{2,4},{3,5}}
 => 5
[1,4,5,3,2] => {{1},{2,4},{3,5}}
 => 5

Description

The number of occurrences of the pattern {{1},{2}} such that 1 is a maximal element. This is the number of pairs

$i\lt j$ in different blocks such that

$i$ is the maximal element of a block.

Matching statistic: St000472

Mapping

Mp00088: Permutations —Kreweras complement⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000472: Permutations ⟶ ℤResult quality: 20% ●values known / values provided: 20%●distinct values known / distinct values provided: 95%

Values

[1,2] => [2,1] => [2,1] => [1,2] => 1
[2,1] => [1,2] => [1,2] => [2,1] => 0
[1,2,3] => [2,3,1] => [3,2,1] => [1,2,3] => 3
[1,3,2] => [2,1,3] => [2,1,3] => [2,3,1] => 2
[2,1,3] => [3,2,1] => [2,3,1] => [2,1,3] => 1
[2,3,1] => [1,2,3] => [1,2,3] => [3,2,1] => 0
[3,1,2] => [3,1,2] => [3,1,2] => [1,3,2] => 1
[3,2,1] => [1,3,2] => [1,3,2] => [3,1,2] => 1
[1,2,3,4] => [2,3,4,1] => [4,3,2,1] => [1,2,3,4] => 6
[1,2,4,3] => [2,3,1,4] => [3,2,1,4] => [2,3,4,1] => 5
[1,3,2,4] => [2,4,3,1] => [3,4,2,1] => [2,1,3,4] => 4
[1,3,4,2] => [2,1,3,4] => [2,1,3,4] => [3,4,2,1] => 3
[1,4,2,3] => [2,4,1,3] => [4,2,1,3] => [1,3,4,2] => 4
[1,4,3,2] => [2,1,4,3] => [2,1,4,3] => [3,4,1,2] => 4
[2,1,3,4] => [3,2,4,1] => [2,4,3,1] => [3,1,2,4] => 3
[2,1,4,3] => [3,2,1,4] => [2,3,1,4] => [3,2,4,1] => 2
[2,3,1,4] => [4,2,3,1] => [2,3,4,1] => [3,2,1,4] => 1
[2,3,4,1] => [1,2,3,4] => [1,2,3,4] => [4,3,2,1] => 0
[2,4,1,3] => [4,2,1,3] => [2,4,1,3] => [3,1,4,2] => 1
[2,4,3,1] => [1,2,4,3] => [1,2,4,3] => [4,3,1,2] => 1
[3,1,2,4] => [3,4,2,1] => [4,2,3,1] => [1,3,2,4] => 3
[3,1,4,2] => [3,1,2,4] => [3,1,2,4] => [2,4,3,1] => 2
[3,2,1,4] => [4,3,2,1] => [3,2,4,1] => [2,3,1,4] => 3
[3,2,4,1] => [1,3,2,4] => [1,3,2,4] => [4,2,3,1] => 2
[3,4,1,2] => [4,1,2,3] => [4,1,2,3] => [1,4,3,2] => 1
[3,4,2,1] => [1,4,2,3] => [1,4,2,3] => [4,1,3,2] => 1
[4,1,2,3] => [3,4,1,2] => [4,1,3,2] => [1,4,2,3] => 3
[4,1,3,2] => [3,1,4,2] => [4,3,1,2] => [1,2,4,3] => 3
[4,2,1,3] => [4,3,1,2] => [3,1,4,2] => [2,4,1,3] => 3
[4,2,3,1] => [1,3,4,2] => [1,4,3,2] => [4,1,2,3] => 3
[4,3,1,2] => [4,1,3,2] => [3,4,1,2] => [2,1,4,3] => 1
[4,3,2,1] => [1,4,3,2] => [1,3,4,2] => [4,2,1,3] => 1
[1,2,3,4,5] => [2,3,4,5,1] => [5,4,3,2,1] => [1,2,3,4,5] => 10
[1,2,3,5,4] => [2,3,4,1,5] => [4,3,2,1,5] => [2,3,4,5,1] => 9
[1,2,4,3,5] => [2,3,5,4,1] => [4,5,3,2,1] => [2,1,3,4,5] => 8
[1,2,4,5,3] => [2,3,1,4,5] => [3,2,1,4,5] => [3,4,5,2,1] => 7
[1,2,5,3,4] => [2,3,5,1,4] => [5,3,2,1,4] => [1,3,4,5,2] => 8
[1,2,5,4,3] => [2,3,1,5,4] => [3,2,1,5,4] => [3,4,5,1,2] => 8
[1,3,2,4,5] => [2,4,3,5,1] => [3,5,4,2,1] => [3,1,2,4,5] => 7
[1,3,2,5,4] => [2,4,3,1,5] => [3,4,2,1,5] => [3,2,4,5,1] => 6
[1,3,4,2,5] => [2,5,3,4,1] => [3,4,5,2,1] => [3,2,1,4,5] => 5
[1,3,4,5,2] => [2,1,3,4,5] => [2,1,3,4,5] => [4,5,3,2,1] => 4
[1,3,5,2,4] => [2,5,3,1,4] => [3,5,2,1,4] => [3,1,4,5,2] => 5
[1,3,5,4,2] => [2,1,3,5,4] => [2,1,3,5,4] => [4,5,3,1,2] => 5
[1,4,2,3,5] => [2,4,5,3,1] => [5,3,4,2,1] => [1,3,2,4,5] => 7
[1,4,2,5,3] => [2,4,1,3,5] => [4,2,1,3,5] => [2,4,5,3,1] => 6
[1,4,3,2,5] => [2,5,4,3,1] => [4,3,5,2,1] => [2,3,1,4,5] => 7
[1,4,3,5,2] => [2,1,4,3,5] => [2,1,4,3,5] => [4,5,2,3,1] => 6
[1,4,5,2,3] => [2,5,1,3,4] => [5,2,1,3,4] => [1,4,5,3,2] => 5
[1,4,5,3,2] => [2,1,5,3,4] => [2,1,5,3,4] => [4,5,1,3,2] => 5
[1,2,3,4,5,7,6] => [2,3,4,5,6,1,7] => [6,5,4,3,2,1,7] => [2,3,4,5,6,7,1] => ? = 20
[1,2,3,4,6,5,7] => [2,3,4,5,7,6,1] => [6,7,5,4,3,2,1] => [2,1,3,4,5,6,7] => ? = 19
[1,2,3,4,6,7,5] => [2,3,4,5,1,6,7] => [5,4,3,2,1,6,7] => [3,4,5,6,7,2,1] => ? = 18
[1,2,3,4,7,6,5] => [2,3,4,5,1,7,6] => [5,4,3,2,1,7,6] => [3,4,5,6,7,1,2] => ? = 19
[1,2,3,5,4,6,7] => [2,3,4,6,5,7,1] => [5,7,6,4,3,2,1] => [3,1,2,4,5,6,7] => ? = 18
[1,2,3,5,4,7,6] => [2,3,4,6,5,1,7] => [5,6,4,3,2,1,7] => [3,2,4,5,6,7,1] => ? = 17
[1,2,3,5,6,4,7] => [2,3,4,7,5,6,1] => [5,6,7,4,3,2,1] => [3,2,1,4,5,6,7] => ? = 16
[1,2,3,5,6,7,4] => [2,3,4,1,5,6,7] => [4,3,2,1,5,6,7] => [4,5,6,7,3,2,1] => ? = 15
[1,2,3,5,7,4,6] => [2,3,4,7,5,1,6] => [5,7,4,3,2,1,6] => [3,1,4,5,6,7,2] => ? = 16
[1,2,3,5,7,6,4] => [2,3,4,1,5,7,6] => [4,3,2,1,5,7,6] => [4,5,6,7,3,1,2] => ? = 16
[1,2,3,6,4,7,5] => [2,3,4,6,1,5,7] => [6,4,3,2,1,5,7] => [2,4,5,6,7,3,1] => ? = 17
[1,2,3,6,5,4,7] => [2,3,4,7,6,5,1] => [6,5,7,4,3,2,1] => [2,3,1,4,5,6,7] => ? = 18
[1,2,3,6,5,7,4] => [2,3,4,1,6,5,7] => [4,3,2,1,6,5,7] => [4,5,6,7,2,3,1] => ? = 17
[1,2,3,6,7,5,4] => [2,3,4,1,7,5,6] => [4,3,2,1,7,5,6] => [4,5,6,7,1,3,2] => ? = 16
[1,2,3,7,5,4,6] => [2,3,4,7,6,1,5] => [6,4,3,2,1,7,5] => [2,4,5,6,7,1,3] => ? = 18
[1,2,3,7,5,6,4] => [2,3,4,1,6,7,5] => [4,3,2,1,7,6,5] => [4,5,6,7,1,2,3] => ? = 18
[1,2,3,7,6,4,5] => [2,3,4,7,1,6,5] => [6,7,4,3,2,1,5] => [2,1,4,5,6,7,3] => ? = 16
[1,2,3,7,6,5,4] => [2,3,4,1,7,6,5] => [4,3,2,1,6,7,5] => [4,5,6,7,2,1,3] => ? = 16
[1,2,4,3,5,6,7] => [2,3,5,4,6,7,1] => [4,7,6,5,3,2,1] => [4,1,2,3,5,6,7] => ? = 17
[1,2,4,3,5,7,6] => [2,3,5,4,6,1,7] => [4,6,5,3,2,1,7] => [4,2,3,5,6,7,1] => ? = 16
[1,2,4,3,6,5,7] => [2,3,5,4,7,6,1] => [4,6,7,5,3,2,1] => [4,2,1,3,5,6,7] => ? = 15
[1,2,4,3,6,7,5] => [2,3,5,4,1,6,7] => [4,5,3,2,1,6,7] => [4,3,5,6,7,2,1] => ? = 14
[1,2,4,3,7,5,6] => [2,3,5,4,7,1,6] => [4,7,5,3,2,1,6] => [4,1,3,5,6,7,2] => ? = 15
[1,2,4,3,7,6,5] => [2,3,5,4,1,7,6] => [4,5,3,2,1,7,6] => [4,3,5,6,7,1,2] => ? = 15
[1,2,4,5,3,6,7] => [2,3,6,4,5,7,1] => [4,5,7,6,3,2,1] => [4,3,1,2,5,6,7] => ? = 14
[1,2,4,5,3,7,6] => [2,3,6,4,5,1,7] => [4,5,6,3,2,1,7] => [4,3,2,5,6,7,1] => ? = 13
[1,2,4,5,6,3,7] => [2,3,7,4,5,6,1] => [4,5,6,7,3,2,1] => [4,3,2,1,5,6,7] => ? = 12
[1,2,4,5,6,7,3] => [2,3,1,4,5,6,7] => [3,2,1,4,5,6,7] => [5,6,7,4,3,2,1] => ? = 11
[1,2,4,5,7,3,6] => [2,3,7,4,5,1,6] => [4,5,7,3,2,1,6] => [4,3,1,5,6,7,2] => ? = 12
[1,2,4,5,7,6,3] => [2,3,1,4,5,7,6] => [3,2,1,4,5,7,6] => [5,6,7,4,3,1,2] => ? = 12
[1,2,4,6,3,5,7] => [2,3,6,4,7,5,1] => [4,7,5,6,3,2,1] => [4,1,3,2,5,6,7] => ? = 14
[1,2,4,6,3,7,5] => [2,3,6,4,1,5,7] => [4,6,3,2,1,5,7] => [4,2,5,6,7,3,1] => ? = 13
[1,2,4,6,5,3,7] => [2,3,7,4,6,5,1] => [4,6,5,7,3,2,1] => [4,2,3,1,5,6,7] => ? = 14
[1,2,4,6,5,7,3] => [2,3,1,4,6,5,7] => [3,2,1,4,6,5,7] => [5,6,7,4,2,3,1] => ? = 13
[1,2,4,6,7,3,5] => [2,3,7,4,1,5,6] => [4,7,3,2,1,5,6] => [4,1,5,6,7,3,2] => ? = 12
[1,2,4,6,7,5,3] => [2,3,1,4,7,5,6] => [3,2,1,4,7,5,6] => [5,6,7,4,1,3,2] => ? = 12
[1,2,4,7,3,5,6] => [2,3,6,4,7,1,5] => [4,7,3,2,1,6,5] => [4,1,5,6,7,2,3] => ? = 14
[1,2,4,7,3,6,5] => [2,3,6,4,1,7,5] => [4,7,6,3,2,1,5] => [4,1,2,5,6,7,3] => ? = 14
[1,2,4,7,5,3,6] => [2,3,7,4,6,1,5] => [4,6,3,2,1,7,5] => [4,2,5,6,7,1,3] => ? = 14
[1,2,4,7,5,6,3] => [2,3,1,4,6,7,5] => [3,2,1,4,7,6,5] => [5,6,7,4,1,2,3] => ? = 14
[1,2,4,7,6,3,5] => [2,3,7,4,1,6,5] => [4,6,7,3,2,1,5] => [4,2,1,5,6,7,3] => ? = 12
[1,2,4,7,6,5,3] => [2,3,1,4,7,6,5] => [3,2,1,4,6,7,5] => [5,6,7,4,2,1,3] => ? = 12
[1,2,5,3,4,7,6] => [2,3,5,6,4,1,7] => [6,4,5,3,2,1,7] => [2,4,3,5,6,7,1] => ? = 16
[1,2,5,3,6,4,7] => [2,3,5,7,4,6,1] => [6,7,4,5,3,2,1] => [2,1,4,3,5,6,7] => ? = 15
[1,2,5,3,6,7,4] => [2,3,5,1,4,6,7] => [5,3,2,1,4,6,7] => [3,5,6,7,4,2,1] => ? = 14
[1,2,5,3,7,6,4] => [2,3,5,1,4,7,6] => [5,3,2,1,4,7,6] => [3,5,6,7,4,1,2] => ? = 15
[1,2,5,4,3,6,7] => [2,3,6,5,4,7,1] => [5,4,7,6,3,2,1] => [3,4,1,2,5,6,7] => ? = 17
[1,2,5,4,3,7,6] => [2,3,6,5,4,1,7] => [5,4,6,3,2,1,7] => [3,4,2,5,6,7,1] => ? = 16
[1,2,5,4,6,3,7] => [2,3,7,5,4,6,1] => [5,4,6,7,3,2,1] => [3,4,2,1,5,6,7] => ? = 15
[1,2,5,4,6,7,3] => [2,3,1,5,4,6,7] => [3,2,1,5,4,6,7] => [5,6,7,3,4,2,1] => ? = 14

Description

The sum of the ascent bottoms of a permutation.