Identifier
Values
[(1,4),(2,3),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
[(1,3),(2,4),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
[(1,3),(2,4),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
[(1,4),(2,3),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => ([(0,2),(0,3),(1,2),(1,3)],4) => 4
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,5),(2,4),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,6),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,5),(2,6),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,3),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,4),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,4),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,5),(3,10),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,10),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,3),(2,4),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,2),(3,4),(5,9),(6,8),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,4),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,9),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,5),(3,9),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,8),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,3),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,5),(2,10),(3,4),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,10),(3,5),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,9),(3,5),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,9),(3,4),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,8),(3,4),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,8),(3,5),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,10),(2,5),(3,4),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,9),(2,5),(3,4),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,8),(2,5),(3,4),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,6),(2,5),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,6),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,6),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,3),(2,6),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,6),(2,4),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,8),(2,4),(3,5),(6,9),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,9),(2,4),(3,5),(6,8),(7,10)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,10),(2,4),(3,5),(6,8),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,6),(2,3),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,5),(2,3),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,3),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,3),(2,4),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,3),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,10),(2,4),(3,5),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,9),(2,4),(3,5),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,8),(2,4),(3,5),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,6),(2,4),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,5),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,3),(2,5),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,6),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,4),(2,6),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,6),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,8),(2,5),(3,4),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,9),(2,5),(3,4),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,8),(3,5),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,8),(3,4),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,9),(3,4),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,9),(3,5),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,10),(3,5),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,10),(3,4),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,4),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,2),(3,4),(5,8),(6,10),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,4),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,8),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,5),(3,8),(6,10),(7,9)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,5),(3,9),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,9),(6,10),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,3),(2,4),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,2),(3,4),(5,9),(6,10),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => ([(0,4),(1,2),(1,3),(2,4),(3,4)],5) => 4
[(1,3),(2,4),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,5),(2,4),(3,10),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,5),(3,10),(6,9),(7,8)] => [1,1,1,0,0,1,1,0,0,0] => [1,4,5,2,3] => ([(1,3),(1,4),(2,3),(2,4)],5) => 4
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
>>> Load all 183 entries. <<<
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => ([(0,1),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) => 4
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) => 4
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [1,1,1,0,0,0,1,1,1,0,0,0] => [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) => 4
[(1,12),(2,3),(4,5),(6,9),(7,10),(8,11)] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,11),(2,3),(4,5),(6,9),(7,10),(8,12)] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,10),(2,3),(4,5),(6,9),(7,11),(8,12)] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,9),(2,3),(4,5),(6,10),(7,11),(8,12)] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,12),(2,4),(3,5),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,4),(3,5),(6,7),(8,10),(9,12)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,4),(3,5),(6,7),(8,11),(9,12)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,4),(3,5),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,11),(2,4),(3,5),(6,8),(7,10),(9,12)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,10),(2,4),(3,5),(6,8),(7,11),(9,12)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,12),(2,4),(3,5),(6,9),(7,10),(8,11)] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,4),(3,5),(6,9),(7,10),(8,12)] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,4),(3,5),(6,9),(7,11),(8,12)] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,4),(3,5),(6,10),(7,11),(8,12)] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,4),(3,6),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,11),(2,4),(3,6),(5,7),(8,10),(9,12)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,10),(2,4),(3,6),(5,7),(8,11),(9,12)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,12),(2,5),(3,6),(4,7),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,11),(2,5),(3,6),(4,7),(8,9),(10,12)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,12),(2,5),(3,6),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,5),(3,6),(4,7),(8,10),(9,12)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,5),(3,6),(4,7),(8,11),(9,12)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,12),(2,5),(3,6),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,11),(2,5),(3,6),(4,9),(7,10),(8,12)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,10),(2,5),(3,6),(4,9),(7,11),(8,12)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,9),(2,5),(3,6),(4,10),(7,11),(8,12)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,3),(2,12),(4,5),(6,9),(7,10),(8,11)] => [1,1,0,1,0,1,1,1,0,0,0,0] => [1,3,5,6,2,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,4),(2,12),(3,5),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,12),(3,5),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,4),(2,12),(3,5),(6,9),(7,10),(8,11)] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,12),(3,6),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,5),(2,12),(3,6),(4,7),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,5),(2,12),(3,6),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,12),(3,6),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,5),(3,12),(6,7),(8,10),(9,11)] => [1,1,1,0,0,1,0,1,1,0,0,0] => [1,4,5,2,3,6] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,5),(3,12),(6,8),(7,10),(9,11)] => [1,1,1,0,0,1,1,0,1,0,0,0] => [1,4,5,2,6,3] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,4),(2,5),(3,12),(6,9),(7,10),(8,11)] => [1,1,1,0,0,1,1,1,0,0,0,0] => [1,4,5,6,2,3] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,4),(2,6),(3,12),(5,7),(8,10),(9,11)] => [1,1,1,0,1,0,0,1,1,0,0,0] => [1,4,6,2,3,5] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,5),(2,6),(3,12),(4,7),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,5),(2,6),(3,12),(4,7),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,6),(3,12),(4,9),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,6),(3,7),(4,12),(8,9),(10,11)] => [1,1,1,1,0,0,0,1,0,1,0,0] => [1,5,2,6,3,4] => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6) => 4
[(1,5),(2,6),(3,7),(4,12),(8,10),(9,11)] => [1,1,1,1,0,0,0,1,1,0,0,0] => [1,5,6,2,3,4] => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) => 4
[(1,5),(2,6),(3,9),(4,12),(7,10),(8,11)] => [1,1,1,1,0,0,1,1,0,0,0,0] => [1,2,5,6,3,4] => ([(2,4),(2,5),(3,4),(3,5)],6) => 4
search for individual values
searching the database for the individual values of this statistic
Description
The girth of a graph, which is not a tree.
This is the length of the shortest cycle in the graph.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
to Dyck path
Description
The Dyck path corresponding to the opener-closer sequence of the perfect matching.
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.