Identifier
Values
[(1,2),(3,4)] => [1,0,1,0] => [1,2] => 1 => 1
[(1,2),(3,4),(5,6)] => [1,0,1,0,1,0] => [1,2,3] => 11 => 2
[(1,3),(2,4),(5,6)] => [1,1,0,0,1,0] => [2,1,3] => 01 => 1
[(1,4),(2,3),(5,6)] => [1,1,0,0,1,0] => [2,1,3] => 01 => 1
[(1,2),(3,5),(4,6)] => [1,0,1,1,0,0] => [1,3,2] => 10 => 1
[(1,2),(3,6),(4,5)] => [1,0,1,1,0,0] => [1,3,2] => 10 => 1
[(1,2),(3,4),(5,6),(7,8)] => [1,0,1,0,1,0,1,0] => [1,2,3,4] => 111 => 3
[(1,3),(2,4),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 011 => 1
[(1,4),(2,3),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => [2,1,3,4] => 011 => 1
[(1,5),(2,3),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 001 => 1
[(1,6),(2,3),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 001 => 1
[(1,6),(2,4),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001 => 1
[(1,5),(2,4),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001 => 1
[(1,4),(2,5),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001 => 1
[(1,3),(2,5),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 001 => 1
[(1,2),(3,5),(4,6),(7,8)] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 101 => 2
[(1,2),(3,6),(4,5),(7,8)] => [1,0,1,1,0,0,1,0] => [1,3,2,4] => 101 => 2
[(1,3),(2,6),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => [2,3,1,4] => 001 => 1
[(1,4),(2,6),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001 => 1
[(1,5),(2,6),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001 => 1
[(1,6),(2,5),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => [3,2,1,4] => 001 => 1
[(1,2),(3,7),(4,5),(6,8)] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 100 => 1
[(1,2),(3,8),(4,5),(6,7)] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 100 => 1
[(1,2),(3,8),(4,6),(5,7)] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100 => 1
[(1,2),(3,7),(4,6),(5,8)] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100 => 1
[(1,2),(3,6),(4,7),(5,8)] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100 => 1
[(1,2),(3,5),(4,7),(6,8)] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 100 => 1
[(1,4),(2,3),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 010 => 1
[(1,3),(2,4),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 010 => 1
[(1,2),(3,4),(5,7),(6,8)] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 110 => 1
[(1,2),(3,4),(5,8),(6,7)] => [1,0,1,0,1,1,0,0] => [1,2,4,3] => 110 => 1
[(1,3),(2,4),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 010 => 1
[(1,4),(2,3),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => [2,1,4,3] => 010 => 1
[(1,2),(3,5),(4,8),(6,7)] => [1,0,1,1,0,1,0,0] => [1,3,4,2] => 100 => 1
[(1,2),(3,6),(4,8),(5,7)] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100 => 1
[(1,2),(3,7),(4,8),(5,6)] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100 => 1
[(1,2),(3,8),(4,7),(5,6)] => [1,0,1,1,1,0,0,0] => [1,4,3,2] => 100 => 1
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [1,0,1,0,1,0,1,0,1,0] => [1,2,3,4,5] => 1111 => 4
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 0111 => 2
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [1,1,0,0,1,0,1,0,1,0] => [2,1,3,4,5] => 0111 => 2
[(1,5),(2,3),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0011 => 1
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0011 => 1
[(1,7),(2,3),(4,5),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,8),(2,4),(3,5),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,7),(2,4),(3,5),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,6),(2,4),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011 => 1
[(1,5),(2,4),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011 => 1
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011 => 1
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0011 => 1
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1011 => 2
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [1,0,1,1,0,0,1,0,1,0] => [1,3,2,4,5] => 1011 => 2
[(1,3),(2,6),(4,5),(7,8),(9,10)] => [1,1,0,1,0,0,1,0,1,0] => [2,3,1,4,5] => 0011 => 1
[(1,4),(2,6),(3,5),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011 => 1
[(1,5),(2,6),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011 => 1
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [1,1,1,0,0,0,1,0,1,0] => [3,2,1,4,5] => 0011 => 1
[(1,7),(2,5),(3,4),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,8),(2,6),(3,4),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,7),(2,6),(3,4),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,6),(2,7),(3,4),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,5),(2,7),(3,4),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,4),(2,7),(3,5),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,3),(2,7),(4,5),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,2),(3,7),(4,5),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 1001 => 2
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 1001 => 2
[(1,3),(2,8),(4,5),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,4),(2,8),(3,5),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,5),(2,8),(3,4),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,6),(2,8),(3,4),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,7),(2,8),(3,4),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,2),(3,9),(4,5),(6,7),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,2),(3,10),(4,6),(5,7),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,9),(4,6),(5,7),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,8),(2,7),(3,5),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,7),(2,8),(3,5),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,6),(2,8),(3,5),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,5),(2,8),(3,6),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,4),(2,8),(3,6),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,3),(2,8),(4,6),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,2),(3,8),(4,6),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001 => 2
[(1,2),(3,7),(4,6),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001 => 2
[(1,3),(2,7),(4,6),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,4),(2,7),(3,6),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,5),(2,7),(3,6),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,6),(2,7),(3,5),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,7),(2,6),(3,5),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,8),(2,6),(3,5),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,8),(2,5),(3,6),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,7),(2,5),(3,6),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,6),(2,5),(3,7),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001 => 2
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 1001 => 2
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,5),(2,4),(3,7),(6,8),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
>>> Load all 276 entries. <<<
[(1,6),(2,4),(3,7),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,7),(2,4),(3,6),(5,8),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,8),(2,4),(3,6),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,8),(2,3),(4,6),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,7),(2,3),(4,6),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,6),(2,3),(4,7),(5,8),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,5),(2,3),(4,7),(6,8),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,4),(2,3),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0101 => 0
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0101 => 0
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1101 => 2
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [1,0,1,0,1,1,0,0,1,0] => [1,2,4,3,5] => 1101 => 2
[(1,3),(2,4),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0101 => 0
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [1,1,0,0,1,1,0,0,1,0] => [2,1,4,3,5] => 0101 => 0
[(1,5),(2,3),(4,8),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,6),(2,3),(4,8),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,7),(2,3),(4,8),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,8),(2,4),(3,7),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,7),(2,4),(3,8),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,6),(2,4),(3,8),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,5),(2,4),(3,8),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,4),(2,5),(3,8),(6,7),(9,10)] => [1,1,1,0,0,1,0,0,1,0] => [3,2,4,1,5] => 0001 => 1
[(1,3),(2,5),(4,8),(6,7),(9,10)] => [1,1,0,1,0,1,0,0,1,0] => [2,3,4,1,5] => 0001 => 1
[(1,2),(3,5),(4,8),(6,7),(9,10)] => [1,0,1,1,0,1,0,0,1,0] => [1,3,4,2,5] => 1001 => 2
[(1,2),(3,6),(4,8),(5,7),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001 => 2
[(1,3),(2,6),(4,8),(5,7),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,4),(2,6),(3,8),(5,7),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,5),(2,6),(3,8),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,6),(2,5),(3,8),(4,7),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,7),(2,5),(3,8),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,8),(2,5),(3,7),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,8),(2,6),(3,7),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,7),(2,6),(3,8),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,6),(2,7),(3,8),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,5),(2,7),(3,8),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,4),(2,7),(3,8),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,3),(2,7),(4,8),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,2),(3,7),(4,8),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001 => 2
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [1,0,1,1,1,0,0,0,1,0] => [1,4,3,2,5] => 1001 => 2
[(1,3),(2,8),(4,7),(5,6),(9,10)] => [1,1,0,1,1,0,0,0,1,0] => [2,4,3,1,5] => 0001 => 1
[(1,4),(2,8),(3,7),(5,6),(9,10)] => [1,1,1,0,1,0,0,0,1,0] => [4,2,3,1,5] => 0001 => 1
[(1,5),(2,8),(3,7),(4,6),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,6),(2,8),(3,7),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,7),(2,8),(3,6),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [1,1,1,1,0,0,0,0,1,0] => [4,3,2,1,5] => 0001 => 1
[(1,2),(3,9),(4,7),(5,6),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,10),(4,8),(5,6),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,9),(4,8),(5,6),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,8),(4,9),(5,6),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,7),(4,9),(5,6),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,6),(4,9),(5,7),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,5),(4,9),(6,7),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,4),(2,3),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,3),(2,4),(5,9),(6,7),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,2),(3,4),(5,9),(6,7),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1100 => 1
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1100 => 1
[(1,3),(2,4),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,2),(3,5),(4,10),(6,7),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,2),(3,6),(4,10),(5,7),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,7),(4,10),(5,6),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,8),(4,10),(5,6),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,9),(4,10),(5,6),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,10),(4,9),(5,7),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,9),(4,10),(5,7),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,8),(4,10),(5,7),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,7),(4,10),(5,8),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,6),(4,10),(5,8),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,5),(4,10),(6,8),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,4),(2,3),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,3),(2,4),(5,10),(6,8),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,2),(3,4),(5,10),(6,8),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100 => 1
[(1,2),(3,4),(5,9),(6,8),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100 => 1
[(1,3),(2,4),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,4),(2,3),(5,9),(6,8),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,2),(3,5),(4,9),(6,8),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,6),(4,9),(5,8),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,7),(4,9),(5,8),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,8),(4,9),(5,7),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,9),(4,8),(5,7),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,10),(4,8),(5,7),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,10),(4,7),(5,8),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,9),(4,7),(5,8),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,8),(4,7),(5,9),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,4),(2,3),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100 => 1
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1100 => 1
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,4),(2,3),(5,7),(6,9),(8,10)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,7),(4,6),(5,9),(8,10)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,8),(4,6),(5,9),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,9),(4,6),(5,8),(7,10)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,10),(4,6),(5,8),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,10),(4,5),(6,8),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,9),(4,5),(6,8),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,8),(4,5),(6,9),(7,10)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,7),(4,5),(6,9),(8,10)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,6),(2,5),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,5),(2,6),(3,4),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,4),(2,6),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,3),(2,6),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,2),(3,6),(4,5),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1010 => 0
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1010 => 0
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,5),(2,4),(3,6),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,6),(2,4),(3,5),(7,9),(8,10)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,6),(2,3),(4,5),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,5),(2,3),(4,6),(7,9),(8,10)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,4),(2,3),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0110 => 2
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0110 => 2
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1110 => 2
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [1,0,1,0,1,0,1,1,0,0] => [1,2,3,5,4] => 1110 => 2
[(1,3),(2,4),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0110 => 2
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [1,1,0,0,1,0,1,1,0,0] => [2,1,3,5,4] => 0110 => 2
[(1,5),(2,3),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,6),(2,4),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,5),(2,4),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,4),(2,5),(3,6),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,3),(2,5),(4,6),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,2),(3,5),(4,6),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1010 => 0
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [1,0,1,1,0,0,1,1,0,0] => [1,3,2,5,4] => 1010 => 0
[(1,3),(2,6),(4,5),(7,10),(8,9)] => [1,1,0,1,0,0,1,1,0,0] => [2,3,1,5,4] => 0010 => 1
[(1,4),(2,6),(3,5),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,5),(2,6),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [1,1,1,0,0,0,1,1,0,0] => [3,2,1,5,4] => 0010 => 1
[(1,2),(3,7),(4,5),(6,10),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,2),(3,8),(4,5),(6,10),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,9),(4,5),(6,10),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,10),(4,6),(5,9),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,9),(4,6),(5,10),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,8),(4,6),(5,10),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,7),(4,6),(5,10),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,6),(4,7),(5,10),(8,9)] => [1,0,1,1,1,0,0,1,0,0] => [1,4,3,5,2] => 1000 => 1
[(1,2),(3,5),(4,7),(6,10),(8,9)] => [1,0,1,1,0,1,0,1,0,0] => [1,3,4,5,2] => 1000 => 1
[(1,4),(2,3),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,3),(2,4),(5,7),(6,10),(8,9)] => [1,1,0,0,1,1,0,1,0,0] => [2,1,4,5,3] => 0100 => 1
[(1,2),(3,4),(5,7),(6,10),(8,9)] => [1,0,1,0,1,1,0,1,0,0] => [1,2,4,5,3] => 1100 => 1
[(1,2),(3,4),(5,8),(6,10),(7,9)] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100 => 1
[(1,3),(2,4),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,4),(2,3),(5,8),(6,10),(7,9)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,2),(3,5),(4,8),(6,10),(7,9)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,6),(4,8),(5,10),(7,9)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,7),(4,8),(5,10),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,8),(4,7),(5,10),(6,9)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,9),(4,7),(5,10),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,10),(4,7),(5,9),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,10),(4,8),(5,9),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,9),(4,8),(5,10),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,8),(4,9),(5,10),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,7),(4,9),(5,10),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,6),(4,9),(5,10),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,5),(4,9),(6,10),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,4),(2,3),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,3),(2,4),(5,9),(6,10),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,2),(3,4),(5,9),(6,10),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100 => 1
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [1,0,1,0,1,1,1,0,0,0] => [1,2,5,4,3] => 1100 => 1
[(1,3),(2,4),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [1,1,0,0,1,1,1,0,0,0] => [2,1,5,4,3] => 0100 => 1
[(1,2),(3,5),(4,10),(6,9),(7,8)] => [1,0,1,1,0,1,1,0,0,0] => [1,3,5,4,2] => 1000 => 1
[(1,2),(3,6),(4,10),(5,9),(7,8)] => [1,0,1,1,1,0,1,0,0,0] => [1,5,3,4,2] => 1000 => 1
[(1,2),(3,7),(4,10),(5,9),(6,8)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,8),(4,10),(5,9),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,9),(4,10),(5,8),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [1,0,1,1,1,1,0,0,0,0] => [1,5,4,3,2] => 1000 => 1
search for individual values
searching the database for the individual values of this statistic
Description
The number of indecomposable projective-injective modules in the algebra corresponding to a subset.
Let $A_n=K[x]/(x^n)$.
We associate to a nonempty subset S of an (n-1)-set the module $M_S$, which is the direct sum of $A_n$-modules with indecomposable non-projective direct summands of dimension $i$ when $i$ is in $S$ (note that such modules have vector space dimension at most n-1). Then the corresponding algebra associated to S is the stable endomorphism ring of $M_S$. We decode the subset as a binary word so that for example the subset $S=\{1,3 \} $ of $\{1,2,3 \}$ is decoded as 101.
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
to Dyck path
Description
The Dyck path corresponding to the opener-closer sequence of the perfect matching.
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..