Identifier
Values
[[]] => [1,0] => [(1,2)] => 0
[[],[]] => [1,0,1,0] => [(1,2),(3,4)] => 0
[[[]]] => [1,1,0,0] => [(1,4),(2,3)] => 1
[[],[],[]] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 0
[[],[[]]] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 1
[[[]],[]] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 1
[[[],[]]] => [1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => 1
[[[[]]]] => [1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => 2
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 0
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 1
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 1
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 1
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 2
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 1
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 1
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 1
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 2
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => 1
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => 2
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => 2
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => 2
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 3
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 0
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 1
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 1
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 1
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 2
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 1
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 1
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 1
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 2
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 1
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 2
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 2
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 2
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 3
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 1
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 1
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 1
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 1
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 2
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 1
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 2
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 1
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 2
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 1
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 2
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 2
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 2
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 3
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => 1
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => 2
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => 2
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => 2
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 3
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => 2
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 2
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => 2
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 3
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => 2
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 3
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 3
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 3
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 4
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 0
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 1
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 1
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 1
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 2
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 1
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 1
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 1
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 2
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 1
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 2
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 2
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 2
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 3
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => 1
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => 1
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => 1
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => 1
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 2
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => 1
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => 2
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => 1
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => 2
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => 1
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => 2
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => 2
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => 2
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 3
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 1
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 2
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 2
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 2
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 3
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 2
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 2
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 2
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 3
>>> Load all 236 entries. <<<
[[],[[[],[],[]]]] => [1,0,1,1,1,0,1,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => 2
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 3
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 3
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 3
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 4
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => 1
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => 1
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => 1
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => 1
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 2
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => 1
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => 1
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => 1
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => 2
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => 1
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 2
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 2
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 2
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 3
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => 1
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => 2
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => 1
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => 2
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => 1
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => 2
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => 1
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 2
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 2
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 2
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => 1
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => 2
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => 2
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => 2
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 3
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => 1
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 2
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 2
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 2
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 3
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => 1
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => 2
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => 2
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 2
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 3
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => 2
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 2
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 2
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 3
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 2
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 3
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 3
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 3
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 4
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => 1
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => 2
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => 2
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => 2
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => 3
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => 2
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => 2
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => 2
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => 3
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => 2
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => 3
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => 3
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => 3
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => 4
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => 2
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => 2
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => 2
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => 2
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => 3
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => 2
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => 3
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => 2
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => 3
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => 2
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => 3
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => 3
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => 3
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => 4
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => 2
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => 3
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => 3
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => 3
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => 4
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => 3
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => 3
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => 3
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => 4
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => 3
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => 4
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => 4
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => 4
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => 5
[[],[[],[[[[]]]]]] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,5),(6,13),(7,12),(8,11),(9,10)] => 4
[[],[[[[[]]]],[]]] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [(1,2),(3,14),(4,11),(5,10),(6,9),(7,8),(12,13)] => 4
[[],[[[],[[],[]]]]] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,9),(10,11)] => 3
[[],[[[],[[[]]]]]] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,6),(7,12),(8,11),(9,10)] => 4
[[],[[[[]],[[]]]]] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,8),(6,7),(9,12),(10,11)] => 3
[[],[[[[],[]],[]]]] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,7),(8,9),(11,12)] => 3
[[],[[[[[]]],[]]]] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [(1,2),(3,14),(4,13),(5,10),(6,9),(7,8),(11,12)] => 4
[[],[[[[],[],[]]]]] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,9),(10,11)] => 3
[[],[[[[],[[]]]]]] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,7),(8,11),(9,10)] => 4
[[],[[[[[]],[]]]]] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,9),(7,8),(10,11)] => 4
[[],[[[[[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,8),(9,10)] => 4
[[],[[[[[[]]]]]]] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [(1,2),(3,14),(4,13),(5,12),(6,11),(7,10),(8,9)] => 5
[[[]],[[[[[]]]]]] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [(1,4),(2,3),(5,14),(6,13),(7,12),(8,11),(9,10)] => 4
[[[[[[]]]]],[[]]] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,14),(12,13)] => 4
[[[],[[[[]]]]],[]] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8),(13,14)] => 4
[[[[[[]]]],[]],[]] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11),(13,14)] => 4
[[[[],[[],[]]]],[]] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9),(13,14)] => 3
[[[[],[[[]]]]],[]] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8),(13,14)] => 4
[[[[[]],[[]]]],[]] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9),(13,14)] => 3
[[[[[],[]],[]]],[]] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10),(13,14)] => 3
[[[[[[]]],[]]],[]] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10),(13,14)] => 4
[[[[[],[],[]]]],[]] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9),(13,14)] => 3
[[[[[],[[]]]]],[]] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8),(13,14)] => 4
[[[[[[]],[]]]],[]] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9),(13,14)] => 4
[[[[[[],[]]]]],[]] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8),(13,14)] => 4
[[[[[[[]]]]]],[]] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7),(13,14)] => 5
[[],[[[[],[[[]]]]]]] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,7),(8,13),(9,12),(10,11)] => 5
[[],[[[[[[]]],[]]]]] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,11),(7,10),(8,9),(12,13)] => 5
[[],[[[[[],[],[]]]]]] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,10),(11,12)] => 4
[[],[[[[[],[[]]]]]]] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,8),(9,12),(10,11)] => 5
[[],[[[[[[]],[]]]]]] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,10),(8,9),(11,12)] => 5
[[],[[[[[[],[]]]]]]] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,9),(10,11)] => 5
[[],[[[[[[[]]]]]]]] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,2),(3,16),(4,15),(5,14),(6,13),(7,12),(8,11),(9,10)] => 6
[[[[[],[[[]]]]]],[]] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9),(15,16)] => 5
[[[[[[[]]],[]]]],[]] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11),(15,16)] => 5
[[[[[[],[],[]]]]],[]] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10),(15,16)] => 4
[[[[[[],[[]]]]]],[]] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9),(15,16)] => 5
[[[[[[[]],[]]]]],[]] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10),(15,16)] => 5
[[[[[[[],[]]]]]],[]] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9),(15,16)] => 5
[[[[[[[[]]]]]]],[]] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8),(15,16)] => 6
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Description
The maximal number of arcs nesting a given arc of a perfect matching.
This is also the largest weight of a down step in the histoire d'Hermite corresponding to the perfect matching.
Map
to Dyck path
Description
Return the Dyck path of the corresponding ordered tree induced by the recurrence of the Catalan numbers, see wikipedia:Catalan_number.
This sends the maximal height of the Dyck path to the depth of the tree.
Map
to tunnel matching
Description
Sends a Dyck path of semilength n to the noncrossing perfect matching given by matching an up-step with the corresponding down-step.
This is, for a Dyck path $D$ of semilength $n$, the perfect matching of $\{1,\dots,2n\}$ with $i < j$ being matched if $D_i$ is an up-step and $D_j$ is the down-step connected to $D_i$ by a tunnel.