Identifier
Values
[[]] => [1,0] => [(1,2)] => 1
[[],[]] => [1,0,1,0] => [(1,2),(3,4)] => 1
[[[]]] => [1,1,0,0] => [(1,4),(2,3)] => 2
[[],[],[]] => [1,0,1,0,1,0] => [(1,2),(3,4),(5,6)] => 1
[[],[[]]] => [1,0,1,1,0,0] => [(1,2),(3,6),(4,5)] => 2
[[[]],[]] => [1,1,0,0,1,0] => [(1,4),(2,3),(5,6)] => 2
[[[],[]]] => [1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => 2
[[[[]]]] => [1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => 3
[[],[],[],[]] => [1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8)] => 1
[[],[],[[]]] => [1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7)] => 2
[[],[[]],[]] => [1,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,8)] => 2
[[],[[],[]]] => [1,0,1,1,0,1,0,0] => [(1,2),(3,8),(4,5),(6,7)] => 2
[[],[[[]]]] => [1,0,1,1,1,0,0,0] => [(1,2),(3,8),(4,7),(5,6)] => 3
[[[]],[],[]] => [1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8)] => 2
[[[]],[[]]] => [1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7)] => 2
[[[],[]],[]] => [1,1,0,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,8)] => 2
[[[[]]],[]] => [1,1,1,0,0,0,1,0] => [(1,6),(2,5),(3,4),(7,8)] => 3
[[[],[],[]]] => [1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => 2
[[[],[[]]]] => [1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => 3
[[[[]],[]]] => [1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => 3
[[[[],[]]]] => [1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => 3
[[[[[]]]]] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 4
[[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10)] => 1
[[],[],[],[[]]] => [1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,10),(8,9)] => 2
[[],[],[[]],[]] => [1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10)] => 2
[[],[],[[],[]]] => [1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,10),(6,7),(8,9)] => 2
[[],[],[[[]]]] => [1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,10),(6,9),(7,8)] => 3
[[],[[]],[],[]] => [1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10)] => 2
[[],[[]],[[]]] => [1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,10),(8,9)] => 2
[[],[[],[]],[]] => [1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10)] => 2
[[],[[[]]],[]] => [1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10)] => 3
[[],[[],[],[]]] => [1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,10),(4,5),(6,7),(8,9)] => 2
[[],[[],[[]]]] => [1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,10),(4,5),(6,9),(7,8)] => 3
[[],[[[]],[]]] => [1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,10),(4,7),(5,6),(8,9)] => 3
[[],[[[],[]]]] => [1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,10),(4,9),(5,6),(7,8)] => 3
[[],[[[[]]]]] => [1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,10),(4,9),(5,8),(6,7)] => 4
[[[]],[],[],[]] => [1,1,0,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10)] => 2
[[[]],[],[[]]] => [1,1,0,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,10),(8,9)] => 2
[[[]],[[]],[]] => [1,1,0,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10)] => 2
[[[]],[[],[]]] => [1,1,0,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,10),(6,7),(8,9)] => 2
[[[]],[[[]]]] => [1,1,0,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,10),(6,9),(7,8)] => 3
[[[],[]],[],[]] => [1,1,0,1,0,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10)] => 2
[[[[]]],[],[]] => [1,1,1,0,0,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10)] => 3
[[[],[]],[[]]] => [1,1,0,1,0,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,10),(8,9)] => 2
[[[[]]],[[]]] => [1,1,1,0,0,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,10),(8,9)] => 3
[[[],[],[]],[]] => [1,1,0,1,0,1,0,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10)] => 2
[[[],[[]]],[]] => [1,1,0,1,1,0,0,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10)] => 3
[[[[]],[]],[]] => [1,1,1,0,0,1,0,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10)] => 3
[[[[],[]]],[]] => [1,1,1,0,1,0,0,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10)] => 3
[[[[[]]]],[]] => [1,1,1,1,0,0,0,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10)] => 4
[[[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => 2
[[[],[],[[]]]] => [1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => 3
[[[],[[]],[]]] => [1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => 3
[[[],[[],[]]]] => [1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => 3
[[[],[[[]]]]] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 4
[[[[]],[],[]]] => [1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => 3
[[[[]],[[]]]] => [1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 3
[[[[],[]],[]]] => [1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => 3
[[[[[]]],[]]] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 4
[[[[],[],[]]]] => [1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => 3
[[[[],[[]]]]] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 4
[[[[[]],[]]]] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 4
[[[[[],[]]]]] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 4
[[[[[[]]]]]] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 5
[[],[],[],[],[],[]] => [1,0,1,0,1,0,1,0,1,0,1,0] => [(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => 1
[[],[],[],[],[[]]] => [1,0,1,0,1,0,1,0,1,1,0,0] => [(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => 2
[[],[],[],[[]],[]] => [1,0,1,0,1,0,1,1,0,0,1,0] => [(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => 2
[[],[],[],[[],[]]] => [1,0,1,0,1,0,1,1,0,1,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => 2
[[],[],[],[[[]]]] => [1,0,1,0,1,0,1,1,1,0,0,0] => [(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => 3
[[],[],[[]],[],[]] => [1,0,1,0,1,1,0,0,1,0,1,0] => [(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => 2
[[],[],[[]],[[]]] => [1,0,1,0,1,1,0,0,1,1,0,0] => [(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => 2
[[],[],[[],[]],[]] => [1,0,1,0,1,1,0,1,0,0,1,0] => [(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => 2
[[],[],[[[]]],[]] => [1,0,1,0,1,1,1,0,0,0,1,0] => [(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => 3
[[],[],[[],[],[]]] => [1,0,1,0,1,1,0,1,0,1,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => 2
[[],[],[[],[[]]]] => [1,0,1,0,1,1,0,1,1,0,0,0] => [(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => 3
[[],[],[[[]],[]]] => [1,0,1,0,1,1,1,0,0,1,0,0] => [(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => 3
[[],[],[[[],[]]]] => [1,0,1,0,1,1,1,0,1,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => 3
[[],[],[[[[]]]]] => [1,0,1,0,1,1,1,1,0,0,0,0] => [(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => 4
[[],[[]],[],[],[]] => [1,0,1,1,0,0,1,0,1,0,1,0] => [(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => 2
[[],[[]],[],[[]]] => [1,0,1,1,0,0,1,0,1,1,0,0] => [(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => 2
[[],[[]],[[]],[]] => [1,0,1,1,0,0,1,1,0,0,1,0] => [(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => 2
[[],[[]],[[],[]]] => [1,0,1,1,0,0,1,1,0,1,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => 2
[[],[[]],[[[]]]] => [1,0,1,1,0,0,1,1,1,0,0,0] => [(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => 3
[[],[[],[]],[],[]] => [1,0,1,1,0,1,0,0,1,0,1,0] => [(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => 2
[[],[[[]]],[],[]] => [1,0,1,1,1,0,0,0,1,0,1,0] => [(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => 3
[[],[[],[]],[[]]] => [1,0,1,1,0,1,0,0,1,1,0,0] => [(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => 2
[[],[[[]]],[[]]] => [1,0,1,1,1,0,0,0,1,1,0,0] => [(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => 3
[[],[[],[],[]],[]] => [1,0,1,1,0,1,0,1,0,0,1,0] => [(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => 2
[[],[[],[[]]],[]] => [1,0,1,1,0,1,1,0,0,0,1,0] => [(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => 3
[[],[[[]],[]],[]] => [1,0,1,1,1,0,0,1,0,0,1,0] => [(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => 3
[[],[[[],[]]],[]] => [1,0,1,1,1,0,1,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => 3
[[],[[[[]]]],[]] => [1,0,1,1,1,1,0,0,0,0,1,0] => [(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => 4
[[],[[],[],[],[]]] => [1,0,1,1,0,1,0,1,0,1,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => 2
[[],[[],[],[[]]]] => [1,0,1,1,0,1,0,1,1,0,0,0] => [(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => 3
[[],[[],[[]],[]]] => [1,0,1,1,0,1,1,0,0,1,0,0] => [(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => 3
[[],[[],[[],[]]]] => [1,0,1,1,0,1,1,0,1,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => 3
[[],[[],[[[]]]]] => [1,0,1,1,0,1,1,1,0,0,0,0] => [(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => 4
[[],[[[]],[],[]]] => [1,0,1,1,1,0,0,1,0,1,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => 3
[[],[[[]],[[]]]] => [1,0,1,1,1,0,0,1,1,0,0,0] => [(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => 3
[[],[[[],[]],[]]] => [1,0,1,1,1,0,1,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => 3
[[],[[[[]]],[]]] => [1,0,1,1,1,1,0,0,0,1,0,0] => [(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => 4
>>> 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)] => 3
[[],[[[],[[]]]]] => [1,0,1,1,1,0,1,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => 4
[[],[[[[]],[]]]] => [1,0,1,1,1,1,0,0,1,0,0,0] => [(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => 4
[[],[[[[],[]]]]] => [1,0,1,1,1,1,0,1,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => 4
[[],[[[[[]]]]]] => [1,0,1,1,1,1,1,0,0,0,0,0] => [(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => 5
[[[]],[],[],[],[]] => [1,1,0,0,1,0,1,0,1,0,1,0] => [(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => 2
[[[]],[],[],[[]]] => [1,1,0,0,1,0,1,0,1,1,0,0] => [(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => 2
[[[]],[],[[]],[]] => [1,1,0,0,1,0,1,1,0,0,1,0] => [(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => 2
[[[]],[],[[],[]]] => [1,1,0,0,1,0,1,1,0,1,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => 2
[[[]],[],[[[]]]] => [1,1,0,0,1,0,1,1,1,0,0,0] => [(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => 3
[[[]],[[]],[],[]] => [1,1,0,0,1,1,0,0,1,0,1,0] => [(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => 2
[[[]],[[]],[[]]] => [1,1,0,0,1,1,0,0,1,1,0,0] => [(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => 2
[[[]],[[],[]],[]] => [1,1,0,0,1,1,0,1,0,0,1,0] => [(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => 2
[[[]],[[[]]],[]] => [1,1,0,0,1,1,1,0,0,0,1,0] => [(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => 3
[[[]],[[],[],[]]] => [1,1,0,0,1,1,0,1,0,1,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => 2
[[[]],[[],[[]]]] => [1,1,0,0,1,1,0,1,1,0,0,0] => [(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => 3
[[[]],[[[]],[]]] => [1,1,0,0,1,1,1,0,0,1,0,0] => [(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => 3
[[[]],[[[],[]]]] => [1,1,0,0,1,1,1,0,1,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => 3
[[[]],[[[[]]]]] => [1,1,0,0,1,1,1,1,0,0,0,0] => [(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => 4
[[[],[]],[],[],[]] => [1,1,0,1,0,0,1,0,1,0,1,0] => [(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => 2
[[[[]]],[],[],[]] => [1,1,1,0,0,0,1,0,1,0,1,0] => [(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => 3
[[[],[]],[],[[]]] => [1,1,0,1,0,0,1,0,1,1,0,0] => [(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => 2
[[[[]]],[],[[]]] => [1,1,1,0,0,0,1,0,1,1,0,0] => [(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => 3
[[[],[]],[[]],[]] => [1,1,0,1,0,0,1,1,0,0,1,0] => [(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => 2
[[[[]]],[[]],[]] => [1,1,1,0,0,0,1,1,0,0,1,0] => [(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => 3
[[[],[]],[[],[]]] => [1,1,0,1,0,0,1,1,0,1,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => 2
[[[],[]],[[[]]]] => [1,1,0,1,0,0,1,1,1,0,0,0] => [(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => 3
[[[[]]],[[],[]]] => [1,1,1,0,0,0,1,1,0,1,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => 3
[[[[]]],[[[]]]] => [1,1,1,0,0,0,1,1,1,0,0,0] => [(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => 3
[[[],[],[]],[],[]] => [1,1,0,1,0,1,0,0,1,0,1,0] => [(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => 2
[[[],[[]]],[],[]] => [1,1,0,1,1,0,0,0,1,0,1,0] => [(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => 3
[[[[]],[]],[],[]] => [1,1,1,0,0,1,0,0,1,0,1,0] => [(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => 3
[[[[],[]]],[],[]] => [1,1,1,0,1,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => 3
[[[[[]]]],[],[]] => [1,1,1,1,0,0,0,0,1,0,1,0] => [(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => 4
[[[],[],[]],[[]]] => [1,1,0,1,0,1,0,0,1,1,0,0] => [(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => 2
[[[],[[]]],[[]]] => [1,1,0,1,1,0,0,0,1,1,0,0] => [(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => 3
[[[[]],[]],[[]]] => [1,1,1,0,0,1,0,0,1,1,0,0] => [(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => 3
[[[[],[]]],[[]]] => [1,1,1,0,1,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => 3
[[[[[]]]],[[]]] => [1,1,1,1,0,0,0,0,1,1,0,0] => [(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => 4
[[[],[],[],[]],[]] => [1,1,0,1,0,1,0,1,0,0,1,0] => [(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => 2
[[[],[],[[]]],[]] => [1,1,0,1,0,1,1,0,0,0,1,0] => [(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => 3
[[[],[[]],[]],[]] => [1,1,0,1,1,0,0,1,0,0,1,0] => [(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => 3
[[[],[[],[]]],[]] => [1,1,0,1,1,0,1,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => 3
[[[],[[[]]]],[]] => [1,1,0,1,1,1,0,0,0,0,1,0] => [(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => 4
[[[[]],[],[]],[]] => [1,1,1,0,0,1,0,1,0,0,1,0] => [(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => 3
[[[[]],[[]]],[]] => [1,1,1,0,0,1,1,0,0,0,1,0] => [(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => 3
[[[[],[]],[]],[]] => [1,1,1,0,1,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => 3
[[[[[]]],[]],[]] => [1,1,1,1,0,0,0,1,0,0,1,0] => [(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => 4
[[[[],[],[]]],[]] => [1,1,1,0,1,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => 3
[[[[],[[]]]],[]] => [1,1,1,0,1,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => 4
[[[[[]],[]]],[]] => [1,1,1,1,0,0,1,0,0,0,1,0] => [(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => 4
[[[[[],[]]]],[]] => [1,1,1,1,0,1,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => 4
[[[[[[]]]]],[]] => [1,1,1,1,1,0,0,0,0,0,1,0] => [(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => 5
[[[],[],[],[],[]]] => [1,1,0,1,0,1,0,1,0,1,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => 2
[[[],[],[],[[]]]] => [1,1,0,1,0,1,0,1,1,0,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => 3
[[[],[],[[]],[]]] => [1,1,0,1,0,1,1,0,0,1,0,0] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => 3
[[[],[],[[],[]]]] => [1,1,0,1,0,1,1,0,1,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => 3
[[[],[],[[[]]]]] => [1,1,0,1,0,1,1,1,0,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => 4
[[[],[[]],[],[]]] => [1,1,0,1,1,0,0,1,0,1,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => 3
[[[],[[]],[[]]]] => [1,1,0,1,1,0,0,1,1,0,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => 3
[[[],[[],[]],[]]] => [1,1,0,1,1,0,1,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => 3
[[[],[[[]]],[]]] => [1,1,0,1,1,1,0,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => 4
[[[],[[],[],[]]]] => [1,1,0,1,1,0,1,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => 3
[[[],[[],[[]]]]] => [1,1,0,1,1,0,1,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => 4
[[[],[[[]],[]]]] => [1,1,0,1,1,1,0,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => 4
[[[],[[[],[]]]]] => [1,1,0,1,1,1,0,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => 4
[[[],[[[[]]]]]] => [1,1,0,1,1,1,1,0,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => 5
[[[[]],[],[],[]]] => [1,1,1,0,0,1,0,1,0,1,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => 3
[[[[]],[],[[]]]] => [1,1,1,0,0,1,0,1,1,0,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => 3
[[[[]],[[]],[]]] => [1,1,1,0,0,1,1,0,0,1,0,0] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => 3
[[[[]],[[],[]]]] => [1,1,1,0,0,1,1,0,1,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => 3
[[[[]],[[[]]]]] => [1,1,1,0,0,1,1,1,0,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => 4
[[[[],[]],[],[]]] => [1,1,1,0,1,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => 3
[[[[[]]],[],[]]] => [1,1,1,1,0,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => 4
[[[[],[]],[[]]]] => [1,1,1,0,1,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => 3
[[[[[]]],[[]]]] => [1,1,1,1,0,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => 4
[[[[],[],[]],[]]] => [1,1,1,0,1,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => 3
[[[[],[[]]],[]]] => [1,1,1,0,1,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => 4
[[[[[]],[]],[]]] => [1,1,1,1,0,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => 4
[[[[[],[]]],[]]] => [1,1,1,1,0,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => 4
[[[[[[]]]],[]]] => [1,1,1,1,1,0,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => 5
[[[[],[],[],[]]]] => [1,1,1,0,1,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => 3
[[[[],[],[[]]]]] => [1,1,1,0,1,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => 4
[[[[],[[]],[]]]] => [1,1,1,0,1,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => 4
[[[[],[[],[]]]]] => [1,1,1,0,1,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => 4
[[[[],[[[]]]]]] => [1,1,1,0,1,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => 5
[[[[[]],[],[]]]] => [1,1,1,1,0,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => 4
[[[[[]],[[]]]]] => [1,1,1,1,0,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => 4
[[[[[],[]],[]]]] => [1,1,1,1,0,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => 4
[[[[[[]]],[]]]] => [1,1,1,1,1,0,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => 5
[[[[[],[],[]]]]] => [1,1,1,1,0,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => 4
[[[[[],[[]]]]]] => [1,1,1,1,0,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => 5
[[[[[[]],[]]]]] => [1,1,1,1,1,0,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => 5
[[[[[[],[]]]]]] => [1,1,1,1,1,0,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => 5
[[[[[[[]]]]]]] => [1,1,1,1,1,1,0,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => 6
[[],[[],[[[[]]]]]] => [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)] => 5
[[],[[[[[]]]],[]]] => [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)] => 5
[[],[[[],[[],[]]]]] => [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)] => 4
[[],[[[],[[[]]]]]] => [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)] => 5
[[],[[[[]],[[]]]]] => [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)] => 4
[[],[[[[],[]],[]]]] => [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)] => 4
[[],[[[[[]]],[]]]] => [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)] => 5
[[],[[[[],[],[]]]]] => [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)] => 4
[[],[[[[],[[]]]]]] => [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)] => 5
[[],[[[[[]],[]]]]] => [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)] => 5
[[],[[[[[],[]]]]]] => [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)] => 5
[[],[[[[[[]]]]]]] => [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)] => 6
[[[]],[[[[[]]]]]] => [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)] => 5
[[[[[[]]]]],[[]]] => [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)] => 5
[[[],[[[[]]]]],[]] => [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)] => 5
[[[[[[]]]],[]],[]] => [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)] => 5
[[[[],[[],[]]]],[]] => [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)] => 4
[[[[],[[[]]]]],[]] => [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)] => 5
[[[[[]],[[]]]],[]] => [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)] => 4
[[[[[],[]],[]]],[]] => [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)] => 4
[[[[[[]]],[]]],[]] => [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)] => 5
[[[[[],[],[]]]],[]] => [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)] => 4
[[[[[],[[]]]]],[]] => [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)] => 5
[[[[[[]],[]]]],[]] => [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)] => 5
[[[[[[],[]]]]],[]] => [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)] => 5
[[[[[[[]]]]]],[]] => [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)] => 6
[[],[[[[],[[[]]]]]]] => [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)] => 6
[[],[[[[[[]]],[]]]]] => [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)] => 6
[[],[[[[[],[],[]]]]]] => [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)] => 5
[[],[[[[[],[[]]]]]]] => [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)] => 6
[[],[[[[[[]],[]]]]]] => [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)] => 6
[[],[[[[[[],[]]]]]]] => [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)] => 6
[[],[[[[[[[]]]]]]]] => [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)] => 7
[[[[[],[[[]]]]]],[]] => [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)] => 6
[[[[[[[]]],[]]]],[]] => [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)] => 6
[[[[[[],[],[]]]]],[]] => [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)] => 5
[[[[[[],[[]]]]]],[]] => [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)] => 6
[[[[[[[]],[]]]]],[]] => [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)] => 6
[[[[[[[],[]]]]]],[]] => [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)] => 6
[[[[[[[[]]]]]]],[]] => [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)] => 7
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Description
The size of the largest partition in the oscillating tableau corresponding to the perfect matching.
Equivalently, this is the maximal number of crosses in the corresponding triangular rook filling that can be covered by a rectangle.
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.