Identifier
Values
[1] => [1] => ([],1) => ([],1) => 0
[1,2] => [2,1] => ([(0,1)],2) => ([(0,1)],2) => 0
[2,1] => [1,2] => ([],2) => ([],1) => 0
[1,2,3] => [3,2,1] => ([(0,1),(0,2),(1,2)],3) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[1,3,2] => [2,3,1] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[2,1,3] => [3,1,2] => ([(0,2),(1,2)],3) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[2,3,1] => [1,3,2] => ([(1,2)],3) => ([(0,1)],2) => 0
[3,1,2] => [2,1,3] => ([(1,2)],3) => ([(0,1)],2) => 0
[3,2,1] => [1,2,3] => ([],3) => ([],1) => 0
[1,4,3,2] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[2,3,4,1] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[2,4,1,3] => [3,1,4,2] => ([(0,3),(1,2),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[2,4,3,1] => [1,3,4,2] => ([(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[3,1,4,2] => [2,4,1,3] => ([(0,3),(1,2),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[3,2,1,4] => [4,1,2,3] => ([(0,3),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[3,2,4,1] => [1,4,2,3] => ([(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[3,4,1,2] => [2,1,4,3] => ([(0,3),(1,2)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[3,4,2,1] => [1,2,4,3] => ([(2,3)],4) => ([(0,1)],2) => 0
[4,1,2,3] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[4,1,3,2] => [2,3,1,4] => ([(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[4,2,1,3] => [3,1,2,4] => ([(1,3),(2,3)],4) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[4,2,3,1] => [1,3,2,4] => ([(2,3)],4) => ([(0,1)],2) => 0
[4,3,1,2] => [2,1,3,4] => ([(2,3)],4) => ([(0,1)],2) => 0
[4,3,2,1] => [1,2,3,4] => ([],4) => ([],1) => 0
[2,5,4,3,1] => [1,3,4,5,2] => ([(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[3,4,5,2,1] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[3,5,2,4,1] => [1,4,2,5,3] => ([(1,4),(2,3),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[3,5,4,1,2] => [2,1,4,5,3] => ([(0,1),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[3,5,4,2,1] => [1,2,4,5,3] => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[4,2,5,3,1] => [1,3,5,2,4] => ([(1,4),(2,3),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,3,2,5,1] => [1,5,2,3,4] => ([(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,3,5,1,2] => [2,1,5,3,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,3,5,2,1] => [1,2,5,3,4] => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[4,5,1,3,2] => [2,3,1,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,5,2,1,3] => [3,1,2,5,4] => ([(0,1),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,5,2,3,1] => [1,3,2,5,4] => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[4,5,3,1,2] => [2,1,3,5,4] => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[4,5,3,2,1] => [1,2,3,5,4] => ([(3,4)],5) => ([(0,1)],2) => 0
[5,1,4,3,2] => [2,3,4,1,5] => ([(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,2,3,4,1] => [1,4,3,2,5] => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[5,2,4,1,3] => [3,1,4,2,5] => ([(1,4),(2,3),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,2,4,3,1] => [1,3,4,2,5] => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,3,1,4,2] => [2,4,1,3,5] => ([(1,4),(2,3),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,3,2,1,4] => [4,1,2,3,5] => ([(1,4),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,3,2,4,1] => [1,4,2,3,5] => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,3,4,1,2] => [2,1,4,3,5] => ([(1,4),(2,3)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,3,4,2,1] => [1,2,4,3,5] => ([(3,4)],5) => ([(0,1)],2) => 0
[5,4,1,2,3] => [3,2,1,4,5] => ([(2,3),(2,4),(3,4)],5) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[5,4,1,3,2] => [2,3,1,4,5] => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,4,2,1,3] => [3,1,2,4,5] => ([(2,4),(3,4)],5) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,4,2,3,1] => [1,3,2,4,5] => ([(3,4)],5) => ([(0,1)],2) => 0
[5,4,3,1,2] => [2,1,3,4,5] => ([(3,4)],5) => ([(0,1)],2) => 0
[5,4,3,2,1] => [1,2,3,4,5] => ([],5) => ([],1) => 0
[3,6,5,4,2,1] => [1,2,4,5,6,3] => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,5,6,3,2,1] => [1,2,3,6,5,4] => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[4,6,3,5,2,1] => [1,2,5,3,6,4] => ([(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,6,5,2,3,1] => [1,3,2,5,6,4] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,6,5,3,1,2] => [2,1,3,5,6,4] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[4,6,5,3,2,1] => [1,2,3,5,6,4] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,3,6,4,2,1] => [1,2,4,6,3,5] => ([(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,4,3,6,2,1] => [1,2,6,3,4,5] => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,4,6,2,3,1] => [1,3,2,6,4,5] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,4,6,3,1,2] => [2,1,3,6,4,5] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,4,6,3,2,1] => [1,2,3,6,4,5] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,6,2,4,3,1] => [1,3,4,2,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,6,3,2,4,1] => [1,4,2,3,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,6,3,4,1,2] => [2,1,4,3,6,5] => ([(0,5),(1,4),(2,3)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,6,3,4,2,1] => [1,2,4,3,6,5] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,6,4,1,3,2] => [2,3,1,4,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,6,4,2,1,3] => [3,1,2,4,6,5] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,6,4,2,3,1] => [1,3,2,4,6,5] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,6,4,3,1,2] => [2,1,3,4,6,5] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[5,6,4,3,2,1] => [1,2,3,4,6,5] => ([(4,5)],6) => ([(0,1)],2) => 0
[6,2,5,4,3,1] => [1,3,4,5,2,6] => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,3,4,5,2,1] => [1,2,5,4,3,6] => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[6,3,5,2,4,1] => [1,4,2,5,3,6] => ([(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,3,5,4,1,2] => [2,1,4,5,3,6] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,3,5,4,2,1] => [1,2,4,5,3,6] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,4,2,5,3,1] => [1,3,5,2,4,6] => ([(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,4,3,2,5,1] => [1,5,2,3,4,6] => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,4,3,5,1,2] => [2,1,5,3,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,4,3,5,2,1] => [1,2,5,3,4,6] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,4,5,1,3,2] => [2,3,1,5,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,4,5,2,1,3] => [3,1,2,5,4,6] => ([(1,2),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,4,5,2,3,1] => [1,3,2,5,4,6] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,4,5,3,1,2] => [2,1,3,5,4,6] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,4,5,3,2,1] => [1,2,3,5,4,6] => ([(4,5)],6) => ([(0,1)],2) => 0
[6,5,1,4,3,2] => [2,3,4,1,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,2,3,4,1] => [1,4,3,2,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[6,5,2,4,1,3] => [3,1,4,2,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,2,4,3,1] => [1,3,4,2,5,6] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,5,3,1,4,2] => [2,4,1,3,5,6] => ([(2,5),(3,4),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,3,2,1,4] => [4,1,2,3,5,6] => ([(2,5),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,3,2,4,1] => [1,4,2,3,5,6] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,5,3,4,1,2] => [2,1,4,3,5,6] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,5,3,4,2,1] => [1,2,4,3,5,6] => ([(4,5)],6) => ([(0,1)],2) => 0
[6,5,4,1,2,3] => [3,2,1,4,5,6] => ([(3,4),(3,5),(4,5)],6) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[6,5,4,1,3,2] => [2,3,1,4,5,6] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,5,4,2,1,3] => [3,1,2,4,5,6] => ([(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,5,4,2,3,1] => [1,3,2,4,5,6] => ([(4,5)],6) => ([(0,1)],2) => 0
[6,5,4,3,1,2] => [2,1,3,4,5,6] => ([(4,5)],6) => ([(0,1)],2) => 0
>>> Load all 178 entries. <<<
[6,5,4,3,2,1] => [1,2,3,4,5,6] => ([],6) => ([],1) => 0
[4,7,6,5,3,2,1] => [1,2,3,5,6,7,4] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,6,7,4,3,2,1] => [1,2,3,4,7,6,5] => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[5,7,4,6,3,2,1] => [1,2,3,6,4,7,5] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,7,6,3,4,2,1] => [1,2,4,3,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,7,6,4,2,3,1] => [1,3,2,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,7,6,4,3,1,2] => [2,1,3,4,6,7,5] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[5,7,6,4,3,2,1] => [1,2,3,4,6,7,5] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,4,7,5,3,2,1] => [1,2,3,5,7,4,6] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,4,7,3,2,1] => [1,2,3,7,4,5,6] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,7,3,4,2,1] => [1,2,4,3,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,7,4,2,3,1] => [1,3,2,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,7,4,3,1,2] => [2,1,3,4,7,5,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,5,7,4,3,2,1] => [1,2,3,4,7,5,6] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,7,3,5,4,2,1] => [1,2,4,5,3,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,4,3,5,2,1] => [1,2,5,3,4,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,4,5,2,3,1] => [1,3,2,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,4,5,3,1,2] => [2,1,3,5,4,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,4,5,3,2,1] => [1,2,3,5,4,7,6] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,7,5,2,4,3,1] => [1,3,4,2,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,5,3,2,4,1] => [1,4,2,3,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,5,3,4,1,2] => [2,1,4,3,5,7,6] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,5,3,4,2,1] => [1,2,4,3,5,7,6] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,7,5,4,1,3,2] => [2,3,1,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,5,4,2,1,3] => [3,1,2,4,5,7,6] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[6,7,5,4,2,3,1] => [1,3,2,4,5,7,6] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,7,5,4,3,1,2] => [2,1,3,4,5,7,6] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[6,7,5,4,3,2,1] => [1,2,3,4,5,7,6] => ([(5,6)],7) => ([(0,1)],2) => 0
[7,3,6,5,4,2,1] => [1,2,4,5,6,3,7] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,4,5,6,3,2,1] => [1,2,3,6,5,4,7] => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[7,4,6,3,5,2,1] => [1,2,5,3,6,4,7] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,4,6,5,2,3,1] => [1,3,2,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,4,6,5,3,1,2] => [2,1,3,5,6,4,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,4,6,5,3,2,1] => [1,2,3,5,6,4,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,5,3,6,4,2,1] => [1,2,4,6,3,5,7] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,4,3,6,2,1] => [1,2,6,3,4,5,7] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,4,6,2,3,1] => [1,3,2,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,4,6,3,1,2] => [2,1,3,6,4,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,4,6,3,2,1] => [1,2,3,6,4,5,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,5,6,2,4,3,1] => [1,3,4,2,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,6,3,2,4,1] => [1,4,2,3,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,6,3,4,1,2] => [2,1,4,3,6,5,7] => ([(1,6),(2,5),(3,4)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,6,3,4,2,1] => [1,2,4,3,6,5,7] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,5,6,4,1,3,2] => [2,3,1,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,6,4,2,1,3] => [3,1,2,4,6,5,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,5,6,4,2,3,1] => [1,3,2,4,6,5,7] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,5,6,4,3,1,2] => [2,1,3,4,6,5,7] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,5,6,4,3,2,1] => [1,2,3,4,6,5,7] => ([(5,6)],7) => ([(0,1)],2) => 0
[7,6,2,5,4,3,1] => [1,3,4,5,2,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,3,4,5,2,1] => [1,2,5,4,3,6,7] => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[7,6,3,5,2,4,1] => [1,4,2,5,3,6,7] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,3,5,4,1,2] => [2,1,4,5,3,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,3,5,4,2,1] => [1,2,4,5,3,6,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,4,2,5,3,1] => [1,3,5,2,4,6,7] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,4,3,2,5,1] => [1,5,2,3,4,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,4,3,5,1,2] => [2,1,5,3,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,4,3,5,2,1] => [1,2,5,3,4,6,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,4,5,1,3,2] => [2,3,1,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,4,5,2,1,3] => [3,1,2,5,4,6,7] => ([(2,3),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,4,5,2,3,1] => [1,3,2,5,4,6,7] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,4,5,3,1,2] => [2,1,3,5,4,6,7] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,4,5,3,2,1] => [1,2,3,5,4,6,7] => ([(5,6)],7) => ([(0,1)],2) => 0
[7,6,5,1,4,3,2] => [2,3,4,1,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,5,2,3,4,1] => [1,4,3,2,5,6,7] => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[7,6,5,2,4,1,3] => [3,1,4,2,5,6,7] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,5,2,4,3,1] => [1,3,4,2,5,6,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,5,3,1,4,2] => [2,4,1,3,5,6,7] => ([(3,6),(4,5),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,5,3,2,1,4] => [4,1,2,3,5,6,7] => ([(3,6),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,5),(4,7),(5,7),(6,7)],8) => 0
[7,6,5,3,2,4,1] => [1,4,2,3,5,6,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,5,3,4,1,2] => [2,1,4,3,5,6,7] => ([(3,6),(4,5)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,5,3,4,2,1] => [1,2,4,3,5,6,7] => ([(5,6)],7) => ([(0,1)],2) => 0
[7,6,5,4,1,2,3] => [3,2,1,4,5,6,7] => ([(4,5),(4,6),(5,6)],7) => ([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5) => 1
[7,6,5,4,1,3,2] => [2,3,1,4,5,6,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,5,4,2,1,3] => [3,1,2,4,5,6,7] => ([(4,6),(5,6)],7) => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[7,6,5,4,2,3,1] => [1,3,2,4,5,6,7] => ([(5,6)],7) => ([(0,1)],2) => 0
[7,6,5,4,3,1,2] => [2,1,3,4,5,6,7] => ([(5,6)],7) => ([(0,1)],2) => 0
[7,6,5,4,3,2,1] => [1,2,3,4,5,6,7] => ([],7) => ([],1) => 0
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of join irreducibles minus the rank of a lattice.
A lattice is join-extremal, if this statistic is $0$.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
connected vertex partitions
Description
Sends a graph to the lattice of its connected vertex partitions.
A connected vertex partition of a graph $G = (V,E)$ is a set partition of $V$ such that each part induced a connected subgraph of $G$. The connected vertex partitions of $G$ form a lattice under refinement. If $G = K_n$ is a complete graph, the resulting lattice is the lattice of set partitions on $n$ elements.
In the language of matroid theory, this map sends a graph to the lattice of flats of its graphic matroid. The resulting lattice is a geometric lattice, i.e. it is atomistic and semimodular.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.