Processing math: 22%

Identifier
Values
[1] => [1,0] => [1,0] => ([],1) => 0
[1,2] => [1,0,1,0] => [1,1,0,0] => ([(0,1)],2) => 0
[2,1] => [1,1,0,0] => [1,0,1,0] => ([(0,1)],2) => 0
[1,2,3] => [1,0,1,0,1,0] => [1,1,1,0,0,0] => ([(0,1),(0,2),(1,3),(2,3)],4) => 0
[1,3,2] => [1,0,1,1,0,0] => [1,1,0,0,1,0] => ([(0,2),(2,1)],3) => 0
[2,1,3] => [1,1,0,0,1,0] => [1,0,1,1,0,0] => ([(0,2),(2,1)],3) => 0
[2,3,1] => [1,1,0,1,0,0] => [1,0,1,0,1,0] => ([(0,2),(2,1)],3) => 0
[3,1,2] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => ([(0,2),(2,1)],3) => 0
[3,2,1] => [1,1,1,0,0,0] => [1,1,0,1,0,0] => ([(0,2),(2,1)],3) => 0
[1,2,3,4] => [1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 0
[1,2,4,3] => [1,0,1,0,1,1,0,0] => [1,1,1,0,0,0,1,0] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 0
[1,3,2,4] => [1,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0] => ([(0,3),(2,1),(3,2)],4) => 0
[1,3,4,2] => [1,0,1,1,0,1,0,0] => [1,1,0,0,1,0,1,0] => ([(0,3),(2,1),(3,2)],4) => 0
[1,4,2,3] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 0
[1,4,3,2] => [1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,0] => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 0
[2,1,3,4] => [1,1,0,0,1,0,1,0] => [1,0,1,1,1,0,0,0] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 0
[2,1,4,3] => [1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,0] => ([(0,3),(2,1),(3,2)],4) => 0
[2,3,1,4] => [1,1,0,1,0,0,1,0] => [1,0,1,0,1,1,0,0] => ([(0,3),(2,1),(3,2)],4) => 0
[2,3,4,1] => [1,1,0,1,0,1,0,0] => [1,0,1,0,1,0,1,0] => ([(0,3),(2,1),(3,2)],4) => 0
[2,4,1,3] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => ([(0,3),(2,1),(3,2)],4) => 0
[2,4,3,1] => [1,1,0,1,1,0,0,0] => [1,0,1,1,0,1,0,0] => ([(0,3),(2,1),(3,2)],4) => 0
[3,1,2,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 0
[3,1,4,2] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => ([(0,3),(2,1),(3,2)],4) => 0
[3,2,1,4] => [1,1,1,0,0,0,1,0] => [1,1,0,1,1,0,0,0] => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 0
[3,2,4,1] => [1,1,1,0,0,1,0,0] => [1,1,0,1,0,0,1,0] => ([(0,3),(2,1),(3,2)],4) => 0
[3,4,1,2] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => ([(0,3),(2,1),(3,2)],4) => 0
[3,4,2,1] => [1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,0,0] => ([(0,3),(2,1),(3,2)],4) => 0
[4,1,2,3] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 0
[4,1,3,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 0
[4,2,1,3] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 0
[4,2,3,1] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 0
[4,3,1,2] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 0
[4,3,2,1] => [1,1,1,1,0,0,0,0] => [1,1,1,0,1,0,0,0] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 0
[1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,0,1,1,0,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 0
[1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,0,1,0,1,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 0
[1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => [1,1,0,0,1,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 0
[1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => [1,1,0,0,1,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,3,5,2,4] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,3,5,4,2] => [1,0,1,1,0,1,1,0,0,0] => [1,1,0,0,1,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 0
[1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 0
[1,4,3,2,5] => [1,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,0,0,0] => ([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) => 0
[1,4,3,5,2] => [1,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,0,0,1,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 0
[1,4,5,2,3] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 0
[1,4,5,3,2] => [1,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,0,1,0,0] => ([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) => 0
[2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => [1,0,1,1,1,0,0,0,1,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => [1,0,1,1,0,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,1,5,3,4] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[2,1,5,4,3] => [1,1,0,0,1,1,1,0,0,0] => [1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => [1,0,1,0,1,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 0
[2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,4,5,1] => [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
[2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,3,5,4,1] => [1,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,1,3,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 0
[2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,3,1,5] => [1,1,0,1,1,0,0,0,1,0] => [1,0,1,1,0,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 0
[2,4,3,5,1] => [1,1,0,1,1,0,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,5,1,3] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[2,4,5,3,1] => [1,1,0,1,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[3,1,5,4,2] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[3,2,1,5,4] => [1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[3,2,4,1,5] => [1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,0,0,1,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,4,5,1] => [1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,2,5,1,4] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[3,2,5,4,1] => [1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) => 0
[3,4,1,2,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 0
[3,4,1,5,2] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,2,1,5] => [1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,0,1,1,0,0,0] => ([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) => 0
[3,4,2,5,1] => [1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,5,1,2] => [1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[3,4,5,2,1] => [1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,0] => ([(0,4),(2,3),(3,1),(4,2)],5) => 0
[1,3,2,4,6,5] => [1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,0,1,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[1,3,2,5,4,6] => [1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,0,1,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,2,5,6,4] => [1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,0,1,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,2,6,4,5] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[1,3,4,2,6,5] => [1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,0,1,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,4,5,2,6] => [1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,0,1,0,1,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,4,5,6,2] => [1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,0,1,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,4,6,2,5] => [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),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,4,6,5,2] => [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),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,5,2,6,4] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,5,4,6,2] => [1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,0,1,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,5,6,2,4] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[1,3,5,6,4,2] => [1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,0,1,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,4,3,6,5] => [1,1,0,0,1,1,0,0,1,1,0,0] => [1,0,1,1,0,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,4,5,3,6] => [1,1,0,0,1,1,0,1,0,0,1,0] => [1,0,1,1,0,0,1,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,4,5,6,3] => [1,1,0,0,1,1,0,1,0,1,0,0] => [1,0,1,1,0,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,4,6,3,5] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,1,4,6,5,3] => [1,1,0,0,1,1,0,1,1,0,0,0] => [1,0,1,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,1,4,6,5] => [1,1,0,1,0,0,1,0,1,1,0,0] => [1,0,1,0,1,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,3,1,5,4,6] => [1,1,0,1,0,0,1,1,0,0,1,0] => [1,0,1,0,1,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
>>> Load all 151 entries. <<<
[2,3,1,5,6,4] => [1,1,0,1,0,0,1,1,0,1,0,0] => [1,0,1,0,1,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,1,6,4,5] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => [1,0,1,0,1,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,3,4,1,6,5] => [1,1,0,1,0,1,0,0,1,1,0,0] => [1,0,1,0,1,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,4,5,1,6] => [1,1,0,1,0,1,0,1,0,0,1,0] => [1,0,1,0,1,0,1,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,4,5,6,1] => [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
[2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,4,6,5,1] => [1,1,0,1,0,1,0,1,1,0,0,0] => [1,0,1,0,1,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,5,4,6,1] => [1,1,0,1,0,1,1,0,0,1,0,0] => [1,0,1,0,1,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,5,6,1,4] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,3,5,6,4,1] => [1,1,0,1,0,1,1,0,1,0,0,0] => [1,0,1,0,1,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,1,3,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,4,1,5,3,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,4,1,6,5,3] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,4,3,1,6,5] => [1,1,0,1,1,0,0,0,1,1,0,0] => [1,0,1,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,4,3,5,1,6] => [1,1,0,1,1,0,0,1,0,0,1,0] => [1,0,1,1,0,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,5,6,1] => [1,1,0,1,1,0,0,1,0,1,0,0] => [1,0,1,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,3,6,1,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,4,3,6,5,1] => [1,1,0,1,1,0,0,1,1,0,0,0] => [1,0,1,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[2,4,5,1,6,3] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,5,3,6,1] => [1,1,0,1,1,0,1,0,0,1,0,0] => [1,0,1,1,0,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,5,6,1,3] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[2,4,5,6,3,1] => [1,1,0,1,1,0,1,0,1,0,0,0] => [1,0,1,1,0,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,4,2,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,4,5,2,6] => [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),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,1,4,6,5,2] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,1,6,5] => [1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,0,1,0,0,1,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,5,1,6] => [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),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,5,6,1] => [1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,0,1,0,0,1,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,6,1,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,2,4,6,5,1] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,0,1,0,0,1,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,1,2,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[3,4,1,5,2,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,1,5,6,2] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,1,6,2,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[3,4,1,6,5,2] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[3,4,2,1,6,5] => [1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0,1,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[3,4,2,5,1,6] => [1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,0,1,0,1,0,0,1,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,2,5,6,1] => [1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,0,1,0,1,0,0,1,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,2,6,1,5] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[3,4,2,6,5,1] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => ([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) => 0
[3,4,5,1,6,2] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,5,2,6,1] => [1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,0,1,0,1,0,1,0,0,1,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,5,6,1,2] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 0
[3,4,5,6,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 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
Number of triples of incomparable elements in a finite poset.
For a finite poset this is the number of 3-element sets S \in \binom{P}{3} that are pairwise incomparable.
Map
parallelogram poset
Description
The cell poset of the parallelogram polyomino corresponding to the Dyck path.
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.
This map returns the cell poset of \gamma(D). In this partial order, the cells of the polyomino are the elements and a cell covers those cells with which it shares an edge and which are closer to the origin.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let (c_1, \dots, c_k) be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are c_1, c_1+c_2, \dots, c_1+\dots+c_k.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
peaks-to-valleys
Description
Return the path that has a valley wherever the original path has a peak of height at least one.
More precisely, the height of a valley in the image is the height of the corresponding peak minus 2.
This is also (the inverse of) rowmotion on Dyck paths regarded as order ideals in the triangular poset.