Identifier
Values
[1,1,0,1,0,0] => [1,0,1,0,1,0] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3)],4) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(2,3),(2,4)],5) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => ([(0,3),(1,2),(1,3),(2,4),(3,4)],5) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => ([(0,3),(0,4),(1,3),(1,4),(4,2)],5) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,1),(3,4)],5) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,4),(1,2),(1,3),(2,4)],5) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,0,1,0,0,0] => ([(1,4),(2,3),(2,4)],5) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,5),(1,2),(2,5),(5,3),(5,4)],6) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,5),(1,5),(4,2),(5,3),(5,4)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => ([(2,5),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => ([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => ([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => ([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => ([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => ([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => ([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => ([(0,6),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => ([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => ([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => ([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => ([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => ([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => ([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => ([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => ([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => ([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => ([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
>>> Load all 144 entries. <<<
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,5)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,3),(6,2),(6,3)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => ([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => ([(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,2),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => ([(0,2),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(6,3)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(4,5)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => ([(3,6),(4,5),(4,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => ([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => ([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(4,2),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(1,2),(1,7),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4),(7,5),(7,6)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,7),(6,2),(6,7),(7,3),(7,4)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,5),(1,5),(1,7),(2,6),(2,7),(5,6),(6,3),(6,4),(7,3),(7,4)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,5),(2,6),(2,7),(6,3),(6,4),(7,3),(7,4)],8) => ([(0,2),(2,1)],3) => 0
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,2),(2,1)],3) => 0
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,3),(0,5),(1,7),(3,6),(4,2),(5,1),(5,6),(6,7),(7,4)],8) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,7),(3,6),(4,2),(4,6),(5,3),(5,4),(6,7),(7,1)],8) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => ([(0,3),(0,4),(1,6),(2,5),(2,7),(3,5),(3,7),(4,2),(5,6),(7,1)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => ([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8) => ([(0,2),(2,1)],3) => 0
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(4,3),(5,3),(6,4),(7,4),(7,5)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => ([(0,7),(1,4),(4,7),(5,3),(6,2),(6,5),(7,6)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => ([(0,5),(0,6),(0,7),(1,5),(1,6),(1,7),(2,4),(4,5),(4,6),(4,7),(7,3)],8) => ([(0,3),(2,1),(3,2)],4) => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => ([(0,1),(0,2),(0,3),(0,4),(2,7),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7)],8) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(4,3),(5,2),(5,3),(6,4),(6,5),(7,4),(7,5)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => ([(0,7),(1,3),(1,7),(3,5),(3,6),(5,4),(6,2),(6,4),(7,5),(7,6)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => ([(0,6),(0,7),(1,6),(1,7),(2,3),(2,4),(5,4),(6,2),(6,5),(7,3),(7,5)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => ([(0,1),(0,3),(1,2),(1,7),(2,5),(2,6),(3,6),(3,7),(6,4),(7,4),(7,5)],8) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => ([(0,2),(0,7),(1,6),(1,7),(2,5),(2,6),(5,4),(6,3),(6,4),(7,3),(7,5)],8) => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 0
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => ([(4,7),(5,6),(5,7)],8) => ([(0,2),(2,1)],3) => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => ([(0,7),(1,6),(1,7),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7)],8) => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
search for individual values
searching the database for the individual values of this statistic
Description
Number of indecomposable injective modules with projective dimension 2.
Map
Hessenberg poset
Description
The Hessenberg poset of a Dyck path.
Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.
Map
Delest-Viennot-inverse
Description
Return the Dyck path obtained by applying the inverse of Delest-Viennot's bijection to the corresponding parallelogram polyomino.
Let $D$ be a Dyck path of semilength $n$. The parallelogram polyomino $\gamma(D)$ is defined as follows: let $\tilde D = d_0 d_1 \dots d_{2n+1}$ be the Dyck path obtained by prepending an up step and appending a down step to $D$. Then, the upper path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with even indices, and the lower path of $\gamma(D)$ corresponds to the sequence of steps of $\tilde D$ with odd indices.
The Delest-Viennot bijection $\beta$ returns the parallelogram polyomino, whose column heights are the heights of the peaks of the Dyck path, and the intersection heights between columns are the heights of the valleys of the Dyck path.
This map returns the Dyck path $(\beta^{(-1)}\circ\gamma)(D)$.