- FindStat

Your data matches 6 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)

Matching statistic: St001398
(load all 2 compositions to match this statistic)

Mapping

Mp00065: Permutations —permutation poset⟶ Posets
St001398: Posets ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%

Values

[1] => ([],1)
 => 0
[1,2] => ([(0,1)],2)
 => 0
[2,1] => ([],2)
 => 0
[1,2,3] => ([(0,2),(2,1)],3)
 => 0
[1,3,2] => ([(0,1),(0,2)],3)
 => 1
[2,1,3] => ([(0,2),(1,2)],3)
 => 0
[2,3,1] => ([(1,2)],3)
 => 0
[3,1,2] => ([(1,2)],3)
 => 0
[3,2,1] => ([],3)
 => 0
[1,2,3,4] => ([(0,3),(2,1),(3,2)],4)
 => 0
[1,2,4,3] => ([(0,3),(3,1),(3,2)],4)
 => 2
[1,3,2,4] => ([(0,1),(0,2),(1,3),(2,3)],4)
 => 1
[1,3,4,2] => ([(0,2),(0,3),(3,1)],4)
 => 2
[1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
 => 2
[1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
 => 3
[2,1,3,4] => ([(0,3),(1,3),(3,2)],4)
 => 0
[2,1,4,3] => ([(0,2),(0,3),(1,2),(1,3)],4)
 => 2
[2,3,1,4] => ([(0,3),(1,2),(2,3)],4)
 => 0
[2,3,4,1] => ([(1,2),(2,3)],4)
 => 0
[2,4,1,3] => ([(0,3),(1,2),(1,3)],4)
 => 1
[2,4,3,1] => ([(1,2),(1,3)],4)
 => 1
[3,1,2,4] => ([(0,3),(1,2),(2,3)],4)
 => 0
[3,1,4,2] => ([(0,3),(1,2),(1,3)],4)
 => 1
[3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
 => 0
[3,2,4,1] => ([(1,3),(2,3)],4)
 => 0
[3,4,1,2] => ([(0,3),(1,2)],4)
 => 0
[3,4,2,1] => ([(2,3)],4)
 => 0
[4,1,2,3] => ([(1,2),(2,3)],4)
 => 0
[4,1,3,2] => ([(1,2),(1,3)],4)
 => 1
[4,2,1,3] => ([(1,3),(2,3)],4)
 => 0
[4,2,3,1] => ([(2,3)],4)
 => 0
[4,3,1,2] => ([(2,3)],4)
 => 0
[4,3,2,1] => ([],4)
 => 0
[1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5)
 => 0
[1,2,3,5,4] => ([(0,3),(3,4),(4,1),(4,2)],5)
 => 3
[1,2,4,3,5] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5)
 => 2
[1,2,4,5,3] => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 4
[1,2,5,3,4] => ([(0,4),(3,2),(4,1),(4,3)],5)
 => 4
[1,2,5,4,3] => ([(0,4),(4,1),(4,2),(4,3)],5)
 => 6
[1,3,2,4,5] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5)
 => 1
[1,3,2,5,4] => ([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 4
[1,3,4,2,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 2
[1,3,4,5,2] => ([(0,2),(0,4),(3,1),(4,3)],5)
 => 3
[1,3,5,2,4] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 4
[1,3,5,4,2] => ([(0,3),(0,4),(4,1),(4,2)],5)
 => 5
[1,4,2,3,5] => ([(0,2),(0,3),(1,4),(2,4),(3,1)],5)
 => 2
[1,4,2,5,3] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5)
 => 4
[1,4,3,2,5] => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)
 => 3
[1,4,3,5,2] => ([(0,1),(0,2),(0,3),(2,4),(3,4)],5)
 => 4
[1,4,5,2,3] => ([(0,3),(0,4),(3,2),(4,1)],5)
 => 4

Description

Number of subsets of size 3 of elements in a poset that form a "v". For a finite poset

$(P,\leq)$ , this is the number of sets

$\{x,y,z\} \in \binom{P}{3}$ that form a "v"-subposet (i.e., a subposet consisting of a bottom element covered by two incomparable elements).

Matching statistic: St000220
(load all 5 compositions to match this statistic)

Mapping

St000220: Permutations ⟶ ℤResult quality: 32% ●values known / values provided: 32%●distinct values known / distinct values provided: 81%

Values

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

Description

The number of occurrences of the pattern 132 in a permutation.

Matching statistic: St000218
(load all 2 compositions to match this statistic)

Mapping

Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
St000218: Permutations ⟶ ℤResult quality: 32% ●values known / values provided: 32%●distinct values known / distinct values provided: 90%

Values

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

Description

The number of occurrences of the pattern 213 in a permutation.

Matching statistic: St000217
(load all 4 compositions to match this statistic)

Mapping

Mp00069: Permutations —complement⟶ Permutations
St000217: Permutations ⟶ ℤResult quality: 30% ●values known / values provided: 30%●distinct values known / distinct values provided: 57%

Values

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

Description

The number of occurrences of the pattern 312 in a permutation.

Matching statistic: St000219
(load all 3 compositions to match this statistic)

Mapping

Mp00064: Permutations —reverse⟶ Permutations
St000219: Permutations ⟶ ℤResult quality: 29% ●values known / values provided: 29%●distinct values known / distinct values provided: 57%

Values

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

Description

The number of occurrences of the pattern 231 in a permutation.

Matching statistic: St001898
(load all 2 compositions to match this statistic)

Mapping

Mp00305: Permutations —parking function⟶ Parking functions
Mp00290: Parking functions —to ordered set partition⟶ Ordered set partitions
St001898: Ordered set partitions ⟶ ℤResult quality: 24% ●values known / values provided: 24%●distinct values known / distinct values provided: 57%

Values

[1] => [1] => [{1}] => 0
[1,2] => [1,2] => [{1},{2}] => 0
[2,1] => [2,1] => [{2},{1}] => 0
[1,2,3] => [1,2,3] => [{1},{2},{3}] => 0
[1,3,2] => [1,3,2] => [{1},{3},{2}] => 1
[2,1,3] => [2,1,3] => [{2},{1},{3}] => 0
[2,3,1] => [2,3,1] => [{3},{1},{2}] => 0
[3,1,2] => [3,1,2] => [{2},{3},{1}] => 0
[3,2,1] => [3,2,1] => [{3},{2},{1}] => 0
[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}] => 2
[1,3,2,4] => [1,3,2,4] => [{1},{3},{2},{4}] => 1
[1,3,4,2] => [1,3,4,2] => [{1},{4},{2},{3}] => 2
[1,4,2,3] => [1,4,2,3] => [{1},{3},{4},{2}] => 2
[1,4,3,2] => [1,4,3,2] => [{1},{4},{3},{2}] => 3
[2,1,3,4] => [2,1,3,4] => [{2},{1},{3},{4}] => 0
[2,1,4,3] => [2,1,4,3] => [{2},{1},{4},{3}] => 2
[2,3,1,4] => [2,3,1,4] => [{3},{1},{2},{4}] => 0
[2,3,4,1] => [2,3,4,1] => [{4},{1},{2},{3}] => 0
[2,4,1,3] => [2,4,1,3] => [{3},{1},{4},{2}] => 1
[2,4,3,1] => [2,4,3,1] => [{4},{1},{3},{2}] => 1
[3,1,2,4] => [3,1,2,4] => [{2},{3},{1},{4}] => 0
[3,1,4,2] => [3,1,4,2] => [{2},{4},{1},{3}] => 1
[3,2,1,4] => [3,2,1,4] => [{3},{2},{1},{4}] => 0
[3,2,4,1] => [3,2,4,1] => [{4},{2},{1},{3}] => 0
[3,4,1,2] => [3,4,1,2] => [{3},{4},{1},{2}] => 0
[3,4,2,1] => [3,4,2,1] => [{4},{3},{1},{2}] => 0
[4,1,2,3] => [4,1,2,3] => [{2},{3},{4},{1}] => 0
[4,1,3,2] => [4,1,3,2] => [{2},{4},{3},{1}] => 1
[4,2,1,3] => [4,2,1,3] => [{3},{2},{4},{1}] => 0
[4,2,3,1] => [4,2,3,1] => [{4},{2},{3},{1}] => 0
[4,3,1,2] => [4,3,1,2] => [{3},{4},{2},{1}] => 0
[4,3,2,1] => [4,3,2,1] => [{4},{3},{2},{1}] => 0
[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}] => 3
[1,2,4,3,5] => [1,2,4,3,5] => [{1},{2},{4},{3},{5}] => 2
[1,2,4,5,3] => [1,2,4,5,3] => [{1},{2},{5},{3},{4}] => 4
[1,2,5,3,4] => [1,2,5,3,4] => [{1},{2},{4},{5},{3}] => 4
[1,2,5,4,3] => [1,2,5,4,3] => [{1},{2},{5},{4},{3}] => 6
[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}] => 4
[1,3,4,2,5] => [1,3,4,2,5] => [{1},{4},{2},{3},{5}] => 2
[1,3,4,5,2] => [1,3,4,5,2] => [{1},{5},{2},{3},{4}] => 3
[1,3,5,2,4] => [1,3,5,2,4] => [{1},{4},{2},{5},{3}] => 4
[1,3,5,4,2] => [1,3,5,4,2] => [{1},{5},{2},{4},{3}] => 5
[1,4,2,3,5] => [1,4,2,3,5] => [{1},{3},{4},{2},{5}] => 2
[1,4,2,5,3] => [1,4,2,5,3] => [{1},{3},{5},{2},{4}] => 4
[1,4,3,2,5] => [1,4,3,2,5] => [{1},{4},{3},{2},{5}] => 3
[1,4,3,5,2] => [1,4,3,5,2] => [{1},{5},{3},{2},{4}] => 4
[1,4,5,2,3] => [1,4,5,2,3] => [{1},{4},{5},{2},{3}] => 4
[5,4,3,2,6,1] => [5,4,3,2,6,1] => [{6},{4},{3},{2},{1},{5}] => ? = 0
[5,4,3,6,1,2] => [5,4,3,6,1,2] => [{5},{6},{3},{2},{1},{4}] => ? = 0
[5,4,3,6,2,1] => [5,4,3,6,2,1] => [{6},{5},{3},{2},{1},{4}] => ? = 0
[5,4,6,1,2,3] => [5,4,6,1,2,3] => [{4},{5},{6},{2},{1},{3}] => ? = 0
[5,4,6,1,3,2] => [5,4,6,1,3,2] => [{4},{6},{5},{2},{1},{3}] => ? = 1
[5,4,6,2,1,3] => [5,4,6,2,1,3] => [{5},{4},{6},{2},{1},{3}] => ? = 0
[5,4,6,2,3,1] => [5,4,6,2,3,1] => [{6},{4},{5},{2},{1},{3}] => ? = 0
[5,4,6,3,1,2] => [5,4,6,3,1,2] => [{5},{6},{4},{2},{1},{3}] => ? = 0
[5,4,6,3,2,1] => [5,4,6,3,2,1] => [{6},{5},{4},{2},{1},{3}] => ? = 0
[5,6,1,2,3,4] => [5,6,1,2,3,4] => [{3},{4},{5},{6},{1},{2}] => ? = 0
[5,6,1,2,4,3] => [5,6,1,2,4,3] => [{3},{4},{6},{5},{1},{2}] => ? = 2
[5,6,1,3,2,4] => [5,6,1,3,2,4] => [{3},{5},{4},{6},{1},{2}] => ? = 1
[5,6,1,3,4,2] => [5,6,1,3,4,2] => [{3},{6},{4},{5},{1},{2}] => ? = 2
[5,6,1,4,2,3] => [5,6,1,4,2,3] => [{3},{5},{6},{4},{1},{2}] => ? = 2
[5,6,1,4,3,2] => [5,6,1,4,3,2] => [{3},{6},{5},{4},{1},{2}] => ? = 3
[5,6,2,1,3,4] => [5,6,2,1,3,4] => [{4},{3},{5},{6},{1},{2}] => ? = 0
[5,6,2,1,4,3] => [5,6,2,1,4,3] => [{4},{3},{6},{5},{1},{2}] => ? = 2
[5,6,2,3,1,4] => [5,6,2,3,1,4] => [{5},{3},{4},{6},{1},{2}] => ? = 0
[5,6,2,3,4,1] => [5,6,2,3,4,1] => [{6},{3},{4},{5},{1},{2}] => ? = 0
[5,6,2,4,1,3] => [5,6,2,4,1,3] => [{5},{3},{6},{4},{1},{2}] => ? = 1
[5,6,2,4,3,1] => [5,6,2,4,3,1] => [{6},{3},{5},{4},{1},{2}] => ? = 1
[5,6,3,1,2,4] => [5,6,3,1,2,4] => [{4},{5},{3},{6},{1},{2}] => ? = 0
[5,6,3,1,4,2] => [5,6,3,1,4,2] => [{4},{6},{3},{5},{1},{2}] => ? = 1
[5,6,3,2,1,4] => [5,6,3,2,1,4] => [{5},{4},{3},{6},{1},{2}] => ? = 0
[5,6,3,2,4,1] => [5,6,3,2,4,1] => [{6},{4},{3},{5},{1},{2}] => ? = 0
[5,6,3,4,1,2] => [5,6,3,4,1,2] => [{5},{6},{3},{4},{1},{2}] => ? = 0
[5,6,3,4,2,1] => [5,6,3,4,2,1] => [{6},{5},{3},{4},{1},{2}] => ? = 0
[5,6,4,1,2,3] => [5,6,4,1,2,3] => [{4},{5},{6},{3},{1},{2}] => ? = 0
[5,6,4,1,3,2] => [5,6,4,1,3,2] => [{4},{6},{5},{3},{1},{2}] => ? = 1
[5,6,4,2,1,3] => [5,6,4,2,1,3] => [{5},{4},{6},{3},{1},{2}] => ? = 0
[5,6,4,2,3,1] => [5,6,4,2,3,1] => [{6},{4},{5},{3},{1},{2}] => ? = 0
[5,6,4,3,1,2] => [5,6,4,3,1,2] => [{5},{6},{4},{3},{1},{2}] => ? = 0
[5,6,4,3,2,1] => [5,6,4,3,2,1] => [{6},{5},{4},{3},{1},{2}] => ? = 0
[6,1,2,3,4,5] => [6,1,2,3,4,5] => [{2},{3},{4},{5},{6},{1}] => ? = 0
[6,1,2,3,5,4] => [6,1,2,3,5,4] => [{2},{3},{4},{6},{5},{1}] => ? = 3
[6,1,2,4,3,5] => [6,1,2,4,3,5] => [{2},{3},{5},{4},{6},{1}] => ? = 2
[6,1,2,4,5,3] => [6,1,2,4,5,3] => [{2},{3},{6},{4},{5},{1}] => ? = 4
[6,1,2,5,3,4] => [6,1,2,5,3,4] => [{2},{3},{5},{6},{4},{1}] => ? = 4
[6,1,2,5,4,3] => [6,1,2,5,4,3] => [{2},{3},{6},{5},{4},{1}] => ? = 6
[6,1,3,2,4,5] => [6,1,3,2,4,5] => [{2},{4},{3},{5},{6},{1}] => ? = 1
[6,1,3,2,5,4] => [6,1,3,2,5,4] => [{2},{4},{3},{6},{5},{1}] => ? = 4
[6,1,3,4,2,5] => [6,1,3,4,2,5] => [{2},{5},{3},{4},{6},{1}] => ? = 2
[6,1,3,4,5,2] => [6,1,3,4,5,2] => [{2},{6},{3},{4},{5},{1}] => ? = 3
[6,1,3,5,2,4] => [6,1,3,5,2,4] => [{2},{5},{3},{6},{4},{1}] => ? = 4
[6,1,3,5,4,2] => [6,1,3,5,4,2] => [{2},{6},{3},{5},{4},{1}] => ? = 5
[6,1,4,2,3,5] => [6,1,4,2,3,5] => [{2},{4},{5},{3},{6},{1}] => ? = 2
[6,1,4,2,5,3] => [6,1,4,2,5,3] => [{2},{4},{6},{3},{5},{1}] => ? = 4
[6,1,4,3,2,5] => [6,1,4,3,2,5] => [{2},{5},{4},{3},{6},{1}] => ? = 3
[6,1,4,3,5,2] => [6,1,4,3,5,2] => [{2},{6},{4},{3},{5},{1}] => ? = 4
[6,1,4,5,2,3] => [6,1,4,5,2,3] => [{2},{5},{6},{3},{4},{1}] => ? = 4

Description

The number of occurrences of an 132 pattern in an ordered set partition. An occurrence of a pattern

$\pi\in\mathfrak S_k$ ordered set partition with blocks

$B_1|\dots|B_\ell$ is a sequence of elements

$e_1,\dots,e_k$ with

$e_i\in B_{j_i}$ and

$j_1 < \dots < j_k$ order-isomorphic to

$\pi$ .