searching the database
Your data matches 8 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
(click to perform a complete search on your data)
Matching statistic: St001232
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00199: Dyck paths —prime Dyck path⟶ Dyck paths
St001232: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => [1]
=> [1,0,1,0]
=> [1,1,0,1,0,0]
=> 2
[1,2] => [2]
=> [1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 2
[2,1] => [1,1]
=> [1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 4
[1,2,3] => [3]
=> [1,1,1,0,0,0,1,0]
=> [1,1,1,1,0,0,0,1,0,0]
=> 2
[3,2,1] => [1,1,1]
=> [1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 6
[1,2,3,4] => [4]
=> [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,1,1,0,0,0,0,1,0,0]
=> 2
[2,1,4,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 4
[2,4,1,3] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 4
[3,1,4,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 4
[3,4,1,2] => [2,2]
=> [1,1,0,0,1,1,0,0]
=> [1,1,1,0,0,1,1,0,0,0]
=> 4
[4,3,2,1] => [1,1,1,1]
=> [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,1,1,1,0,0,0,0,0]
=> 8
[1,2,3,4,5] => [5]
=> [1,1,1,1,1,0,0,0,0,0,1,0]
=> [1,1,1,1,1,1,0,0,0,0,0,1,0,0]
=> 2
[5,4,3,2,1] => [1,1,1,1,1]
=> [1,0,1,1,1,1,1,0,0,0,0,0]
=> [1,1,0,1,1,1,1,1,0,0,0,0,0,0]
=> 10
[2,1,4,3,6,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,1,4,6,3,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,1,5,3,6,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,1,5,6,3,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,4,1,3,6,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,4,1,6,3,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,4,6,1,3,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,5,1,3,6,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,5,1,6,3,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[2,5,6,1,3,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,1,4,2,6,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,1,4,6,2,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,1,5,2,6,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,1,5,6,2,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,2,1,6,5,4] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[3,2,6,1,5,4] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[3,2,6,5,1,4] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[3,4,1,2,6,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,4,1,6,2,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,4,6,1,2,5] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,5,1,2,6,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,5,1,6,2,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,5,6,1,2,4] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[3,6,2,1,5,4] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[3,6,2,5,1,4] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[4,1,5,2,6,3] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[4,1,5,6,2,3] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[4,2,1,6,5,3] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[4,2,6,1,5,3] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[4,2,6,5,1,3] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[4,3,1,6,5,2] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[4,3,6,1,5,2] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[4,3,6,5,1,2] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
[4,5,1,2,6,3] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[4,5,1,6,2,3] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[4,5,6,1,2,3] => [3,3]
=> [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,1,1,0,0,0]
=> 4
[4,6,2,1,5,3] => [2,2,2]
=> [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,0,0,1,1,1,0,0,0,0]
=> 6
Description
The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.
Matching statistic: St001632
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
[1] => ([],1)
=> ([],1)
=> ([],1)
=> ? = 2 - 8
[1,2] => ([],2)
=> ([],2)
=> ([],1)
=> ? = 2 - 8
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> ? = 4 - 8
[1,2,3] => ([],3)
=> ([],3)
=> ([],1)
=> ? = 2 - 8
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> ? = 6 - 8
[1,2,3,4] => ([],4)
=> ([],4)
=> ([],1)
=> ? = 2 - 8
[2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,3),(1,2)],4)
=> ([],4)
=> ? = 4 - 8
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2)],4)
=> ? = 4 - 8
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2),(2,3)],4)
=> ([(0,3),(1,2)],4)
=> ? = 4 - 8
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([],2)
=> ? = 4 - 8
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> ? = 8 - 8
[1,2,3,4,5] => ([],5)
=> ([],5)
=> ([],1)
=> ? = 2 - 8
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> ? = 10 - 8
[2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ([],6)
=> ? = 4 - 8
[2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],4)
=> ? = 4 - 8
[2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ? = 4 - 8
[2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3)],6)
=> ? = 4 - 8
[3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([],6)
=> ? = 6 - 8
[3,2,6,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ? = 6 - 8
[3,2,6,5,1,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ? = 6 - 8
[3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],4)
=> ? = 4 - 8
[3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([],6)
=> ? = 4 - 8
[3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([],6)
=> ? = 4 - 8
[3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ? = 6 - 8
[3,6,2,5,1,4] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,5),(1,4),(4,2),(5,3)],6)
=> ? = 6 - 8
[4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(2,5),(3,4)],6)
=> ? = 4 - 8
[4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[4,2,1,6,5,3] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(1,2)],4)
=> ? = 6 - 8
[4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,4),(0,5),(1,2),(1,3)],6)
=> ? = 6 - 8
[4,2,6,5,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(2,3),(2,4)],5)
=> ? = 6 - 8
[4,3,1,6,5,2] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,3),(1,2)],4)
=> ? = 6 - 8
[4,3,6,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(2,3),(2,4)],5)
=> ? = 6 - 8
[4,3,6,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([],5)
=> ? = 6 - 8
[4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(4,5)],6)
=> ? = 4 - 8
[4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([],6)
=> ? = 4 - 8
[4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([],2)
=> ? = 4 - 8
[4,6,2,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(2,3),(2,4)],5)
=> ? = 6 - 8
[1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,2,4,7,6,5,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,2,5,7,6,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,2,6,5,4,3,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,2,6,5,4,7,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,2,6,5,7,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,2,6,7,5,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,2,7,3,6,5,4] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,2,7,4,6,5,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,2,7,5,4,3,6] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,2,7,5,4,6,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,2,7,5,6,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,2,7,6,3,5,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,2,7,6,4,3,5] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,2,7,6,4,5,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,2,7,6,5,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,3,4,7,6,5,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,3,6,5,4,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,3,6,5,4,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,3,6,7,5,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,3,7,5,4,2,6] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 0 = 8 - 8
[1,3,7,5,6,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,3,7,6,4,2,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 0 = 8 - 8
[1,3,7,6,4,5,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,4,5,7,6,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,4,6,5,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,4,6,5,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,4,6,7,5,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,4,7,5,3,2,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 0 = 8 - 8
[1,4,7,5,6,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,5,4,3,2,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,5,4,3,6,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,5,4,3,6,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,5,4,6,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,5,4,6,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,5,6,4,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,5,6,4,3,7,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,5,6,4,7,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,5,6,7,4,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,6,2,5,4,3,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,6,2,5,4,7,3] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 0 = 8 - 8
[1,6,2,5,7,4,3] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 0 = 8 - 8
[1,6,3,5,4,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,6,4,3,2,5,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,6,4,3,5,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,6,4,5,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,4),(2,4),(3,4)],5)
=> 0 = 8 - 8
[1,6,4,5,3,7,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,5),(3,4),(5,4)],6)
=> 0 = 8 - 8
[1,6,4,5,7,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,6,5,2,4,3,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)
=> 0 = 8 - 8
[1,6,5,2,4,7,3] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
=> ([(0,4),(1,3),(2,3),(2,4),(3,5),(4,5)],6)
=> 0 = 8 - 8
Description
The number of indecomposable injective modules $I$ with $dim Ext^1(I,A)=1$ for the incidence algebra A of a poset.
Matching statistic: St000422
(load all 10 compositions to match this statistic)
(load all 10 compositions to match this statistic)
Values
[1] => ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 2
[1,2] => ([],2)
=> ([],1)
=> ([(0,1)],2)
=> 2
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[1,2,3] => ([],3)
=> ([],1)
=> ([(0,1)],2)
=> 2
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[1,2,3,4] => ([],4)
=> ([],1)
=> ([(0,1)],2)
=> 2
[2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
[1,2,3,4,5] => ([],5)
=> ([],1)
=> ([(0,1)],2)
=> 2
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 10
[2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,2,6,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,2,6,5,1,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,6,2,5,1,4] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,2,1,6,5,3] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,2,6,5,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,3,1,6,5,2] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,3,6,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,3,6,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,6,2,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,4,7,6,5,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,5,7,6,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,4,3,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,4,7,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,7,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,7,5,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,3,6,5,4] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,4,6,5,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,4,3,6] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,4,6,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,6,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,3,5,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,4,3,5] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,4,5,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,5,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,4,7,6,5,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,5,7,6,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,4,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,4,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,7,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,7,5,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,4,6,5,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,4,2,6] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,4,6,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,6,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,6,4,2,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,6,4,5,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,5,7,6,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,3,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,7,5,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,3,2,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,3,6,2] => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,6,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,2,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,6,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,6,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,3,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,3,7,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,7,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,7,4,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,4,3,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,4,7,3] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,7,4,3] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,3,5,4,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
Description
The energy of a graph, if it is integral.
The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3].
The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.
Matching statistic: St000915
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
[1] => ([],1)
=> ([],1)
=> ([(0,1)],2)
=> 2
[1,2] => ([],2)
=> ([],1)
=> ([(0,1)],2)
=> 2
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[1,2,3] => ([],3)
=> ([],1)
=> ([(0,1)],2)
=> 2
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[1,2,3,4] => ([],4)
=> ([],1)
=> ([(0,1)],2)
=> 2
[2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 8
[1,2,3,4,5] => ([],5)
=> ([],1)
=> ([(0,1)],2)
=> 2
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> 10
[2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,2,6,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,2,6,5,1,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[3,6,2,5,1,4] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,2,1,6,5,3] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,2,6,5,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,3,1,6,5,2] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,3,6,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,3,6,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,1)],2)
=> ([(0,1),(0,2),(1,2)],3)
=> 4
[4,6,2,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 6
[1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,4,7,6,5,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,5,7,6,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,4,3,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,4,7,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,7,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,7,5,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,3,6,5,4] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,4,6,5,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,4,3,6] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,4,6,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,6,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,3,5,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,4,3,5] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,4,5,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,5,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,4,7,6,5,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,5,7,6,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,4,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,4,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,7,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,7,5,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,4,6,5,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,4,2,6] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,4,6,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,6,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,6,4,2,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,6,4,5,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,5,7,6,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,3,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,7,5,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,3,2,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,3,6,2] => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,6,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,2,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,6,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,6,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,3,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,3,7,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,7,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,7,4,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,4,3,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,4,7,3] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,7,4,3] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,3,5,4,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
Description
The Ore degree of a graph.
This is the maximal Ore degree of an edge, which is the sum of the degrees of its two endpoints.
Matching statistic: St000301
Values
[1] => ([],1)
=> ([],1)
=> ([],1)
=> 2
[1,2] => ([],2)
=> ([],1)
=> ([],1)
=> 2
[2,1] => ([(0,1)],2)
=> ([(0,1)],2)
=> ([],2)
=> 4
[1,2,3] => ([],3)
=> ([],1)
=> ([],1)
=> 2
[3,2,1] => ([(0,1),(0,2),(1,2)],3)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[1,2,3,4] => ([],4)
=> ([],1)
=> ([],1)
=> 2
[2,1,4,3] => ([(0,3),(1,2)],4)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,4,1,3] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,1,4,2] => ([(0,3),(1,2),(2,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4)
=> ([(0,1)],2)
=> ([],2)
=> 4
[4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> ([],4)
=> 8
[1,2,3,4,5] => ([],5)
=> ([],1)
=> ([],1)
=> 2
[5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ([],5)
=> 10
[2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,1,4,6,3,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,1,5,3,6,4] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,4,1,3,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,4,1,6,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,5,1,3,6,4] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,1,4,2,6,5] => ([(0,1),(2,5),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,1,4,6,2,5] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,1,5,2,6,4] => ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,2,1,6,5,4] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[3,2,6,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[3,2,6,5,1,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[3,6,2,1,5,4] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[3,6,2,5,1,4] => ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[4,2,1,6,5,3] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[4,2,6,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[4,2,6,5,1,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[4,3,1,6,5,2] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[4,3,6,1,5,2] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[4,3,6,5,1,2] => ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[4,5,6,1,2,3] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ([(0,1)],2)
=> ([],2)
=> 4
[4,6,2,1,5,3] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)
=> ([(0,1),(0,2),(1,2)],3)
=> ([],3)
=> 6
[1,2,3,7,6,5,4] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,4,7,6,5,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,5,7,6,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,4,3,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,4,7,3] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,5,7,4,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,6,7,5,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,3,6,5,4] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,4,6,5,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,4,3,6] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,4,6,3] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,5,6,4,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,3,5,4] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,4,3,5] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,4,5,3] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,2,7,6,5,3,4] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,4,7,6,5,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,5,7,6,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,4,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,4,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,5,7,4,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,6,7,5,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,4,6,5,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,4,2,6] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,4,6,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,5,6,4,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,6,4,2,5] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,3,7,6,4,5,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,5,7,6,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,3,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,5,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,6,7,5,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,3,2,6] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,3,6,2] => ([(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,4,7,5,6,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,2,6,7] => ([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,6,2,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,3,6,7,2] => ([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,3,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,3,7,2] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,4,6,7,3,2] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,3,2,7] => ([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,3,7,2] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,4,7,3,2] => ([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,5,6,7,4,3,2] => ([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,4,3,7] => ([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,4,7,3] => ([(1,6),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,2,5,7,4,3] => ([(1,6),(2,4),(2,5),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
[1,6,3,5,4,2,7] => ([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
=> ?
=> ?
=> ? = 8
Description
The number of facets of the stable set polytope of a graph.
The stable set polytope of a graph $G$ is the convex hull of the characteristic vectors of stable (or independent) sets of vertices of $G$ inside $\mathbb{R}^{V(G)}$.
Matching statistic: St000824
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000824: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 71%
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
Mp00081: Standard tableaux —reading word permutation⟶ Permutations
St000824: Permutations ⟶ ℤResult quality: 3% ●values known / values provided: 3%●distinct values known / distinct values provided: 71%
Values
[1] => [1]
=> [[1]]
=> [1] => ? = 2 - 2
[1,2] => [2]
=> [[1,2]]
=> [1,2] => 0 = 2 - 2
[2,1] => [1,1]
=> [[1],[2]]
=> [2,1] => 2 = 4 - 2
[1,2,3] => [3]
=> [[1,2,3]]
=> [1,2,3] => 0 = 2 - 2
[3,2,1] => [1,1,1]
=> [[1],[2],[3]]
=> [3,2,1] => 4 = 6 - 2
[1,2,3,4] => [4]
=> [[1,2,3,4]]
=> [1,2,3,4] => 0 = 2 - 2
[2,1,4,3] => [2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => 2 = 4 - 2
[2,4,1,3] => [2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => 2 = 4 - 2
[3,1,4,2] => [2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => 2 = 4 - 2
[3,4,1,2] => [2,2]
=> [[1,2],[3,4]]
=> [3,4,1,2] => 2 = 4 - 2
[4,3,2,1] => [1,1,1,1]
=> [[1],[2],[3],[4]]
=> [4,3,2,1] => 6 = 8 - 2
[1,2,3,4,5] => [5]
=> [[1,2,3,4,5]]
=> [1,2,3,4,5] => 0 = 2 - 2
[5,4,3,2,1] => [1,1,1,1,1]
=> [[1],[2],[3],[4],[5]]
=> [5,4,3,2,1] => 8 = 10 - 2
[2,1,4,3,6,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,1,4,6,3,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,1,5,3,6,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,1,5,6,3,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,4,1,3,6,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,4,1,6,3,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,4,6,1,3,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,5,1,3,6,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,5,1,6,3,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[2,5,6,1,3,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,1,4,2,6,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,1,4,6,2,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,1,5,2,6,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,1,5,6,2,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,2,1,6,5,4] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[3,2,6,1,5,4] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[3,2,6,5,1,4] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[3,4,1,2,6,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,4,1,6,2,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,4,6,1,2,5] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,5,1,2,6,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,5,1,6,2,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,5,6,1,2,4] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[3,6,2,1,5,4] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[3,6,2,5,1,4] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,1,5,2,6,3] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[4,1,5,6,2,3] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[4,2,1,6,5,3] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,2,6,1,5,3] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,2,6,5,1,3] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,3,1,6,5,2] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,3,6,1,5,2] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,3,6,5,1,2] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,5,1,2,6,3] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[4,5,1,6,2,3] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[4,5,6,1,2,3] => [3,3]
=> [[1,2,3],[4,5,6]]
=> [4,5,6,1,2,3] => 2 = 4 - 2
[4,6,2,1,5,3] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[4,6,2,5,1,3] => [2,2,2]
=> [[1,2],[3,4],[5,6]]
=> [5,6,3,4,1,2] => 4 = 6 - 2
[1,2,3,7,6,5,4] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,4,7,6,5,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,5,7,6,4,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,6,5,4,3,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,6,5,4,7,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,6,5,7,4,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,6,7,5,4,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,3,6,5,4] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,4,6,5,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,5,4,3,6] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,5,4,6,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,5,6,4,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,6,3,5,4] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,6,4,3,5] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,6,4,5,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,2,7,6,5,3,4] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,4,7,6,5,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,5,7,6,4,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,6,5,4,2,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,6,5,4,7,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,6,5,7,4,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,6,7,5,4,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,7,4,6,5,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,7,5,4,2,6] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,7,5,4,6,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,7,5,6,4,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,7,6,4,2,5] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,3,7,6,4,5,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,5,7,6,3,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,6,5,3,2,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,6,5,3,7,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,6,5,7,3,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,6,7,5,3,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,7,5,3,2,6] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,7,5,3,6,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,4,7,5,6,3,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,4,3,2,6,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,4,3,6,2,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,4,3,6,7,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,4,6,3,2,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,4,6,3,7,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,4,6,7,3,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,6,4,3,2,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,6,4,3,7,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,6,4,7,3,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,5,6,7,4,3,2] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,6,2,5,4,3,7] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,6,2,5,4,7,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
[1,6,2,5,7,4,3] => [4,1,1,1]
=> [[1,2,3,4],[5],[6],[7]]
=> [7,6,5,1,2,3,4] => ? = 8 - 2
Description
The sum of the number of descents and the number of recoils of a permutation.
This statistic is the sum of [[St000021]] and [[St000354]].
Matching statistic: St001880
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 14%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001880: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 14%
Values
[1] => [1] => [1] => ([],1)
=> ? = 2 - 7
[1,2] => [1,2] => [2,1] => ([],2)
=> ? = 2 - 7
[2,1] => [2,1] => [1,2] => ([(0,1)],2)
=> ? = 4 - 7
[1,2,3] => [1,3,2] => [3,2,1] => ([],3)
=> ? = 2 - 7
[3,2,1] => [3,2,1] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? = 6 - 7
[1,2,3,4] => [1,4,3,2] => [4,3,2,1] => ([],4)
=> ? = 2 - 7
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ? = 4 - 7
[2,4,1,3] => [2,4,1,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? = 4 - 7
[3,1,4,2] => [3,1,4,2] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? = 4 - 7
[3,4,1,2] => [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? = 4 - 7
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ? = 8 - 7
[1,2,3,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([],5)
=> ? = 2 - 7
[5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 10 - 7
[2,1,4,3,6,5] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 - 7
[2,1,4,6,3,5] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 - 7
[2,1,5,3,6,4] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 - 7
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 - 7
[2,4,1,3,6,5] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 - 7
[2,4,1,6,3,5] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 - 7
[2,4,6,1,3,5] => [2,6,5,1,4,3] => [1,6,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> ? = 4 - 7
[2,5,1,3,6,4] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 - 7
[2,5,1,6,3,4] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 - 7
[2,5,6,1,3,4] => [2,6,5,1,4,3] => [1,6,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> ? = 4 - 7
[3,1,4,2,6,5] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 - 7
[3,1,4,6,2,5] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 - 7
[3,1,5,2,6,4] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 - 7
[3,1,5,6,2,4] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 - 7
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 6 - 7
[3,2,6,1,5,4] => [3,2,6,1,5,4] => [2,1,6,5,3,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 6 - 7
[3,2,6,5,1,4] => [3,2,6,5,1,4] => [2,1,6,4,3,5] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> ? = 6 - 7
[3,4,1,2,6,5] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 - 7
[3,4,1,6,2,5] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 - 7
[3,4,6,1,2,5] => [3,6,5,1,4,2] => [6,1,5,3,2,4] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ? = 4 - 7
[3,5,1,2,6,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 - 7
[3,5,1,6,2,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 - 7
[3,5,6,1,2,4] => [3,6,5,1,4,2] => [6,1,5,3,2,4] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ? = 4 - 7
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [3,1,6,5,2,4] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
=> ? = 6 - 7
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [3,1,6,4,2,5] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
=> ? = 6 - 7
[4,1,5,2,6,3] => [4,1,6,5,3,2] => [6,5,1,4,3,2] => ([(2,3),(2,4),(2,5)],6)
=> ? = 4 - 7
[4,1,5,6,2,3] => [4,1,6,5,3,2] => [6,5,1,4,3,2] => ([(2,3),(2,4),(2,5)],6)
=> ? = 4 - 7
[4,2,1,6,5,3] => [4,2,1,6,5,3] => [2,6,1,5,4,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 6 - 7
[4,2,6,1,5,3] => [4,2,6,1,5,3] => [2,6,1,5,3,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 6 - 7
[4,2,6,5,1,3] => [4,2,6,5,1,3] => [2,6,1,4,3,5] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)
=> ? = 6 - 7
[4,3,1,6,5,2] => [4,3,1,6,5,2] => [6,2,1,5,4,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ? = 6 - 7
[4,3,6,1,5,2] => [4,3,6,1,5,2] => [6,2,1,5,3,4] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> ? = 6 - 7
[4,3,6,5,1,2] => [4,3,6,5,1,2] => [6,2,1,4,3,5] => ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 6 - 7
[4,5,1,2,6,3] => [4,6,1,5,3,2] => [6,5,1,4,2,3] => ([(2,3),(2,4),(4,5)],6)
=> ? = 4 - 7
[4,5,1,6,2,3] => [4,6,1,5,3,2] => [6,5,1,4,2,3] => ([(2,3),(2,4),(4,5)],6)
=> ? = 4 - 7
[4,5,6,1,2,3] => [4,6,5,1,3,2] => [6,5,1,3,2,4] => ([(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 - 7
[4,6,2,1,5,3] => [4,6,2,1,5,3] => [3,6,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)
=> ? = 6 - 7
[2,3,4,7,6,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,5,7,6,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,6,5,4,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,6,5,7,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,6,7,5,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,7,4,6,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,7,5,4,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,7,5,6,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,3,7,6,4,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,4,5,7,6,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,4,6,5,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,4,6,5,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,4,6,7,5,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,4,7,5,3,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,4,7,5,6,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,5,4,3,6,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,5,4,6,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,5,4,6,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,5,6,4,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,5,6,4,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,5,6,7,4,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,6,3,5,4,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,6,3,5,7,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,6,4,3,5,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,6,4,5,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,6,4,5,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,6,5,3,4,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,3,4,6,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,3,5,4,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,3,5,6,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,3,6,4,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,4,3,5,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,4,5,3,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,4,5,6,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,5,3,4,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
[2,7,6,3,4,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 1 = 8 - 7
Description
The number of 2-Gorenstein indecomposable injective modules in the incidence algebra of the lattice.
Matching statistic: St001879
Mp00068: Permutations —Simion-Schmidt map⟶ Permutations
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 14%
Mp00089: Permutations —Inverse Kreweras complement⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
St001879: Posets ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 14%
Values
[1] => [1] => [1] => ([],1)
=> ? = 2 + 17
[1,2] => [1,2] => [2,1] => ([],2)
=> ? = 2 + 17
[2,1] => [2,1] => [1,2] => ([(0,1)],2)
=> ? = 4 + 17
[1,2,3] => [1,3,2] => [3,2,1] => ([],3)
=> ? = 2 + 17
[3,2,1] => [3,2,1] => [2,1,3] => ([(0,2),(1,2)],3)
=> ? = 6 + 17
[1,2,3,4] => [1,4,3,2] => [4,3,2,1] => ([],4)
=> ? = 2 + 17
[2,1,4,3] => [2,1,4,3] => [1,4,3,2] => ([(0,1),(0,2),(0,3)],4)
=> ? = 4 + 17
[2,4,1,3] => [2,4,1,3] => [1,4,2,3] => ([(0,2),(0,3),(3,1)],4)
=> ? = 4 + 17
[3,1,4,2] => [3,1,4,2] => [4,1,3,2] => ([(1,2),(1,3)],4)
=> ? = 4 + 17
[3,4,1,2] => [3,4,1,2] => [4,1,2,3] => ([(1,2),(2,3)],4)
=> ? = 4 + 17
[4,3,2,1] => [4,3,2,1] => [3,2,1,4] => ([(0,3),(1,3),(2,3)],4)
=> ? = 8 + 17
[1,2,3,4,5] => [1,5,4,3,2] => [5,4,3,2,1] => ([],5)
=> ? = 2 + 17
[5,4,3,2,1] => [5,4,3,2,1] => [4,3,2,1,5] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> ? = 10 + 17
[2,1,4,3,6,5] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 + 17
[2,1,4,6,3,5] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 + 17
[2,1,5,3,6,4] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 + 17
[2,1,5,6,3,4] => [2,1,6,5,4,3] => [1,6,5,4,3,2] => ([(0,1),(0,2),(0,3),(0,4),(0,5)],6)
=> ? = 4 + 17
[2,4,1,3,6,5] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 + 17
[2,4,1,6,3,5] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 + 17
[2,4,6,1,3,5] => [2,6,5,1,4,3] => [1,6,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> ? = 4 + 17
[2,5,1,3,6,4] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 + 17
[2,5,1,6,3,4] => [2,6,1,5,4,3] => [1,6,5,4,2,3] => ([(0,2),(0,3),(0,4),(0,5),(5,1)],6)
=> ? = 4 + 17
[2,5,6,1,3,4] => [2,6,5,1,4,3] => [1,6,5,3,2,4] => ([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)
=> ? = 4 + 17
[3,1,4,2,6,5] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 + 17
[3,1,4,6,2,5] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 + 17
[3,1,5,2,6,4] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 + 17
[3,1,5,6,2,4] => [3,1,6,5,4,2] => [6,1,5,4,3,2] => ([(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 4 + 17
[3,2,1,6,5,4] => [3,2,1,6,5,4] => [2,1,6,5,4,3] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 6 + 17
[3,2,6,1,5,4] => [3,2,6,1,5,4] => [2,1,6,5,3,4] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 6 + 17
[3,2,6,5,1,4] => [3,2,6,5,1,4] => [2,1,6,4,3,5] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)
=> ? = 6 + 17
[3,4,1,2,6,5] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 + 17
[3,4,1,6,2,5] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 + 17
[3,4,6,1,2,5] => [3,6,5,1,4,2] => [6,1,5,3,2,4] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ? = 4 + 17
[3,5,1,2,6,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 + 17
[3,5,1,6,2,4] => [3,6,1,5,4,2] => [6,1,5,4,2,3] => ([(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 4 + 17
[3,5,6,1,2,4] => [3,6,5,1,4,2] => [6,1,5,3,2,4] => ([(1,2),(1,3),(1,4),(3,5),(4,5)],6)
=> ? = 4 + 17
[3,6,2,1,5,4] => [3,6,2,1,5,4] => [3,1,6,5,2,4] => ([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)
=> ? = 6 + 17
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [3,1,6,4,2,5] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)
=> ? = 6 + 17
[4,1,5,2,6,3] => [4,1,6,5,3,2] => [6,5,1,4,3,2] => ([(2,3),(2,4),(2,5)],6)
=> ? = 4 + 17
[4,1,5,6,2,3] => [4,1,6,5,3,2] => [6,5,1,4,3,2] => ([(2,3),(2,4),(2,5)],6)
=> ? = 4 + 17
[4,2,1,6,5,3] => [4,2,1,6,5,3] => [2,6,1,5,4,3] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)
=> ? = 6 + 17
[4,2,6,1,5,3] => [4,2,6,1,5,3] => [2,6,1,5,3,4] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)
=> ? = 6 + 17
[4,2,6,5,1,3] => [4,2,6,5,1,3] => [2,6,1,4,3,5] => ([(0,4),(0,5),(1,2),(1,4),(1,5),(4,3),(5,3)],6)
=> ? = 6 + 17
[4,3,1,6,5,2] => [4,3,1,6,5,2] => [6,2,1,5,4,3] => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)
=> ? = 6 + 17
[4,3,6,1,5,2] => [4,3,6,1,5,2] => [6,2,1,5,3,4] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6)
=> ? = 6 + 17
[4,3,6,5,1,2] => [4,3,6,5,1,2] => [6,2,1,4,3,5] => ([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 6 + 17
[4,5,1,2,6,3] => [4,6,1,5,3,2] => [6,5,1,4,2,3] => ([(2,3),(2,4),(4,5)],6)
=> ? = 4 + 17
[4,5,1,6,2,3] => [4,6,1,5,3,2] => [6,5,1,4,2,3] => ([(2,3),(2,4),(4,5)],6)
=> ? = 4 + 17
[4,5,6,1,2,3] => [4,6,5,1,3,2] => [6,5,1,3,2,4] => ([(2,3),(2,4),(3,5),(4,5)],6)
=> ? = 4 + 17
[4,6,2,1,5,3] => [4,6,2,1,5,3] => [3,6,1,5,2,4] => ([(0,3),(0,4),(1,2),(1,4),(1,5),(3,5)],6)
=> ? = 6 + 17
[2,3,4,7,6,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,5,7,6,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,6,5,4,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,6,5,7,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,6,7,5,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,7,4,6,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,7,5,4,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,7,5,6,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,3,7,6,4,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,4,5,7,6,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,4,6,5,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,4,6,5,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,4,6,7,5,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,4,7,5,3,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,4,7,5,6,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,5,4,3,6,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,5,4,6,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,5,4,6,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,5,6,4,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,5,6,4,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,5,6,7,4,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,6,3,5,4,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,6,3,5,7,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,6,4,3,5,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,6,4,5,3,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,6,4,5,7,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,6,5,3,4,7,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,3,4,6,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,3,5,4,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,3,5,6,4,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,3,6,4,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,4,3,5,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,4,5,3,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,4,5,6,3,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,5,3,4,6,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
[2,7,6,3,4,5,1] => [2,7,6,5,4,3,1] => [1,6,5,4,3,2,7] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
=> 25 = 8 + 17
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.
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!