Identifier
Values
[1,0] => [1,1,0,0] => [(1,4),(2,3)] => 1
[1,0,1,0] => [1,1,0,1,0,0] => [(1,6),(2,3),(4,5)] => 2
[1,1,0,0] => [1,1,1,0,0,0] => [(1,6),(2,5),(3,4)] => 3
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => [(1,8),(2,3),(4,5),(6,7)] => 3
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => [(1,8),(2,3),(4,7),(5,6)] => 4
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => [(1,8),(2,5),(3,4),(6,7)] => 4
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => [(1,8),(2,7),(3,4),(5,6)] => 5
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => [(1,8),(2,7),(3,6),(4,5)] => 6
[1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,0] => [(1,10),(2,3),(4,5),(6,7),(8,9)] => 4
[1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,0] => [(1,10),(2,3),(4,5),(6,9),(7,8)] => 5
[1,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,0,0] => [(1,10),(2,3),(4,7),(5,6),(8,9)] => 5
[1,0,1,1,0,1,0,0] => [1,1,0,1,1,0,1,0,0,0] => [(1,10),(2,3),(4,9),(5,6),(7,8)] => 6
[1,0,1,1,1,0,0,0] => [1,1,0,1,1,1,0,0,0,0] => [(1,10),(2,3),(4,9),(5,8),(6,7)] => 7
[1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,0] => [(1,10),(2,5),(3,4),(6,7),(8,9)] => 5
[1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,0] => [(1,10),(2,5),(3,4),(6,9),(7,8)] => 6
[1,1,0,1,0,0,1,0] => [1,1,1,0,1,0,0,1,0,0] => [(1,10),(2,7),(3,4),(5,6),(8,9)] => 6
[1,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,0,0] => [(1,10),(2,9),(3,4),(5,6),(7,8)] => 7
[1,1,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,0,0] => [(1,10),(2,9),(3,4),(5,8),(6,7)] => 8
[1,1,1,0,0,0,1,0] => [1,1,1,1,0,0,0,1,0,0] => [(1,10),(2,7),(3,6),(4,5),(8,9)] => 7
[1,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,0,0,0] => [(1,10),(2,9),(3,6),(4,5),(7,8)] => 8
[1,1,1,0,1,0,0,0] => [1,1,1,1,0,1,0,0,0,0] => [(1,10),(2,9),(3,8),(4,5),(6,7)] => 9
[1,1,1,1,0,0,0,0] => [1,1,1,1,1,0,0,0,0,0] => [(1,10),(2,9),(3,8),(4,7),(5,6)] => 10
[1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => 5
[1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,1,0,0,0] => [(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => 6
[1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,0] => [(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => 6
[1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => 7
[1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,1,1,0,0,0,0] => [(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => 8
[1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => 6
[1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,1,0,0,1,1,0,0,0] => [(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => 7
[1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => 7
[1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => 8
[1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => 9
[1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => [(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => 8
[1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,0,0] => [(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => 9
[1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => 10
[1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => [(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => 11
[1,1,0,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => 6
[1,1,0,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,1,0,0,0] => [(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => 7
[1,1,0,0,1,1,0,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,0] => [(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => 7
[1,1,0,0,1,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => 8
[1,1,0,0,1,1,1,0,0,0] => [1,1,1,0,0,1,1,1,0,0,0,0] => [(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => 9
[1,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => 7
[1,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => 8
[1,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => 8
[1,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => 9
[1,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => 10
[1,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => 9
[1,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => 10
[1,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => 11
[1,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => 12
[1,1,1,0,0,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => 8
[1,1,1,0,0,0,1,1,0,0] => [1,1,1,1,0,0,0,1,1,0,0,0] => [(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => 9
[1,1,1,0,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,0] => [(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => 9
[1,1,1,0,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => 10
[1,1,1,0,0,1,1,0,0,0] => [1,1,1,1,0,0,1,1,0,0,0,0] => [(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => 11
[1,1,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => 10
[1,1,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => 11
[1,1,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => 12
[1,1,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => 13
[1,1,1,1,0,0,0,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,0] => [(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => 11
[1,1,1,1,0,0,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,0,0] => [(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => 12
[1,1,1,1,0,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,0,0,0] => [(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => 13
[1,1,1,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => 14
[1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1,1,0,0,0,0,0,0] => [(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => 15
[1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,9),(10,13),(11,12)] => 7
[1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,11),(9,10),(12,13)] => 7
[1,0,1,0,1,0,1,1,0,1,0,0] => [1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,13),(9,10),(11,12)] => 8
[1,0,1,0,1,0,1,1,1,0,0,0] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,7),(8,13),(9,12),(10,11)] => 9
[1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,5),(6,9),(7,8),(10,11),(12,13)] => 7
[1,0,1,0,1,1,0,0,1,1,0,0] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,5),(6,9),(7,8),(10,13),(11,12)] => 8
[1,0,1,0,1,1,0,1,0,0,1,0] => [1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,11),(7,8),(9,10),(12,13)] => 8
[1,0,1,0,1,1,0,1,0,1,0,0] => [1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,8),(9,10),(11,12)] => 9
[1,0,1,0,1,1,0,1,1,0,0,0] => [1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,8),(9,12),(10,11)] => 10
[1,0,1,0,1,1,1,0,0,0,1,0] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,5),(6,11),(7,10),(8,9),(12,13)] => 9
[1,0,1,0,1,1,1,0,0,1,0,0] => [1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,10),(8,9),(11,12)] => 10
[1,0,1,0,1,1,1,0,1,0,0,0] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,12),(8,9),(10,11)] => 11
[1,0,1,0,1,1,1,1,0,0,0,0] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,5),(6,13),(7,12),(8,11),(9,10)] => 12
[1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,9),(10,11),(12,13)] => 7
[1,0,1,1,0,0,1,0,1,1,0,0] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,9),(10,13),(11,12)] => 8
[1,0,1,1,0,0,1,1,0,0,1,0] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,11),(9,10),(12,13)] => 8
[1,0,1,1,0,0,1,1,0,1,0,0] => [1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,10),(11,12)] => 9
[1,0,1,1,0,0,1,1,1,0,0,0] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [(1,14),(2,3),(4,7),(5,6),(8,13),(9,12),(10,11)] => 10
[1,0,1,1,0,1,0,0,1,0,1,0] => [1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,9),(5,6),(7,8),(10,11),(12,13)] => 8
[1,0,1,1,0,1,0,0,1,1,0,0] => [1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,9),(5,6),(7,8),(10,13),(11,12)] => 9
[1,0,1,1,0,1,0,1,0,0,1,0] => [1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,6),(7,8),(9,10),(12,13)] => 9
[1,0,1,1,0,1,0,1,0,1,0,0] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,8),(9,10),(11,12)] => 10
[1,0,1,1,0,1,0,1,1,0,0,0] => [1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,8),(9,12),(10,11)] => 11
[1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,6),(7,10),(8,9),(12,13)] => 10
[1,0,1,1,0,1,1,0,0,1,0,0] => [1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,10),(8,9),(11,12)] => 11
[1,0,1,1,0,1,1,0,1,0,0,0] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,12),(8,9),(10,11)] => 12
[1,0,1,1,0,1,1,1,0,0,0,0] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,6),(7,12),(8,11),(9,10)] => 13
[1,0,1,1,1,0,0,0,1,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [(1,14),(2,3),(4,9),(5,8),(6,7),(10,11),(12,13)] => 9
[1,0,1,1,1,0,0,0,1,1,0,0] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [(1,14),(2,3),(4,9),(5,8),(6,7),(10,13),(11,12)] => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => [1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,8),(6,7),(9,10),(12,13)] => 10
[1,0,1,1,1,0,0,1,0,1,0,0] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,8),(6,7),(9,10),(11,12)] => 11
[1,0,1,1,1,0,0,1,1,0,0,0] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,8),(6,7),(9,12),(10,11)] => 12
[1,0,1,1,1,0,1,0,0,0,1,0] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,10),(6,7),(8,9),(12,13)] => 11
[1,0,1,1,1,0,1,0,0,1,0,0] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,10),(6,7),(8,9),(11,12)] => 12
[1,0,1,1,1,0,1,0,1,0,0,0] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,7),(8,9),(10,11)] => 13
[1,0,1,1,1,0,1,1,0,0,0,0] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,7),(8,11),(9,10)] => 14
>>> Load all 204 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [(1,14),(2,3),(4,11),(5,10),(6,9),(7,8),(12,13)] => 12
[1,0,1,1,1,1,0,0,0,1,0,0] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [(1,14),(2,3),(4,13),(5,10),(6,9),(7,8),(11,12)] => 13
[1,0,1,1,1,1,0,0,1,0,0,0] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,9),(7,8),(10,11)] => 14
[1,0,1,1,1,1,0,1,0,0,0,0] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,11),(7,8),(9,10)] => 15
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [(1,14),(2,3),(4,13),(5,12),(6,11),(7,10),(8,9)] => 16
[1,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13)] => 7
[1,1,0,0,1,0,1,0,1,1,0,0] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,9),(10,13),(11,12)] => 8
[1,1,0,0,1,0,1,1,0,0,1,0] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,11),(9,10),(12,13)] => 8
[1,1,0,0,1,0,1,1,0,1,0,0] => [1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,13),(9,10),(11,12)] => 9
[1,1,0,0,1,0,1,1,1,0,0,0] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,7),(8,13),(9,12),(10,11)] => 10
[1,1,0,0,1,1,0,0,1,0,1,0] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [(1,14),(2,5),(3,4),(6,9),(7,8),(10,11),(12,13)] => 8
[1,1,0,0,1,1,0,0,1,1,0,0] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [(1,14),(2,5),(3,4),(6,9),(7,8),(10,13),(11,12)] => 9
[1,1,0,0,1,1,0,1,0,0,1,0] => [1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,11),(7,8),(9,10),(12,13)] => 9
[1,1,0,0,1,1,0,1,0,1,0,0] => [1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,8),(9,10),(11,12)] => 10
[1,1,0,0,1,1,0,1,1,0,0,0] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,8),(9,12),(10,11)] => 11
[1,1,0,0,1,1,1,0,0,0,1,0] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [(1,14),(2,5),(3,4),(6,11),(7,10),(8,9),(12,13)] => 10
[1,1,0,0,1,1,1,0,0,1,0,0] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,10),(8,9),(11,12)] => 11
[1,1,0,0,1,1,1,0,1,0,0,0] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,12),(8,9),(10,11)] => 12
[1,1,0,0,1,1,1,1,0,0,0,0] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [(1,14),(2,5),(3,4),(6,13),(7,12),(8,11),(9,10)] => 13
[1,1,0,1,0,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13)] => 8
[1,1,0,1,0,0,1,0,1,1,0,0] => [1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,9),(10,13),(11,12)] => 9
[1,1,0,1,0,0,1,1,0,0,1,0] => [1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,11),(9,10),(12,13)] => 9
[1,1,0,1,0,0,1,1,0,1,0,0] => [1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,13),(9,10),(11,12)] => 10
[1,1,0,1,0,0,1,1,1,0,0,0] => [1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [(1,14),(2,7),(3,4),(5,6),(8,13),(9,12),(10,11)] => 11
[1,1,0,1,0,1,0,0,1,0,1,0] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,4),(5,6),(7,8),(10,11),(12,13)] => 9
[1,1,0,1,0,1,0,0,1,1,0,0] => [1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,4),(5,6),(7,8),(10,13),(11,12)] => 10
[1,1,0,1,0,1,0,1,0,0,1,0] => [1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,6),(7,8),(9,10),(12,13)] => 10
[1,1,0,1,0,1,0,1,0,1,0,0] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,8),(9,10),(11,12)] => 11
[1,1,0,1,0,1,0,1,1,0,0,0] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,8),(9,12),(10,11)] => 12
[1,1,0,1,0,1,1,0,0,0,1,0] => [1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,6),(7,10),(8,9),(12,13)] => 11
[1,1,0,1,0,1,1,0,0,1,0,0] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,10),(8,9),(11,12)] => 12
[1,1,0,1,0,1,1,0,1,0,0,0] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,12),(8,9),(10,11)] => 13
[1,1,0,1,0,1,1,1,0,0,0,0] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,6),(7,12),(8,11),(9,10)] => 14
[1,1,0,1,1,0,0,0,1,0,1,0] => [1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,4),(5,8),(6,7),(10,11),(12,13)] => 10
[1,1,0,1,1,0,0,0,1,1,0,0] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,4),(5,8),(6,7),(10,13),(11,12)] => 11
[1,1,0,1,1,0,0,1,0,0,1,0] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,8),(6,7),(9,10),(12,13)] => 11
[1,1,0,1,1,0,0,1,0,1,0,0] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,8),(6,7),(9,10),(11,12)] => 12
[1,1,0,1,1,0,0,1,1,0,0,0] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,8),(6,7),(9,12),(10,11)] => 13
[1,1,0,1,1,0,1,0,0,0,1,0] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,10),(6,7),(8,9),(12,13)] => 12
[1,1,0,1,1,0,1,0,0,1,0,0] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,10),(6,7),(8,9),(11,12)] => 13
[1,1,0,1,1,0,1,0,1,0,0,0] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,7),(8,9),(10,11)] => 14
[1,1,0,1,1,0,1,1,0,0,0,0] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,7),(8,11),(9,10)] => 15
[1,1,0,1,1,1,0,0,0,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,4),(5,10),(6,9),(7,8),(12,13)] => 13
[1,1,0,1,1,1,0,0,0,1,0,0] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,4),(5,10),(6,9),(7,8),(11,12)] => 14
[1,1,0,1,1,1,0,0,1,0,0,0] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,9),(7,8),(10,11)] => 15
[1,1,0,1,1,1,0,1,0,0,0,0] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,11),(7,8),(9,10)] => 16
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,4),(5,12),(6,11),(7,10),(8,9)] => 17
[1,1,1,0,0,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13)] => 9
[1,1,1,0,0,0,1,0,1,1,0,0] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,9),(10,13),(11,12)] => 10
[1,1,1,0,0,0,1,1,0,0,1,0] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,11),(9,10),(12,13)] => 10
[1,1,1,0,0,0,1,1,0,1,0,0] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,13),(9,10),(11,12)] => 11
[1,1,1,0,0,0,1,1,1,0,0,0] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [(1,14),(2,7),(3,6),(4,5),(8,13),(9,12),(10,11)] => 12
[1,1,1,0,0,1,0,0,1,0,1,0] => [1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,6),(4,5),(7,8),(10,11),(12,13)] => 10
[1,1,1,0,0,1,0,0,1,1,0,0] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,6),(4,5),(7,8),(10,13),(11,12)] => 11
[1,1,1,0,0,1,0,1,0,0,1,0] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,6),(4,5),(7,8),(9,10),(12,13)] => 11
[1,1,1,0,0,1,0,1,0,1,0,0] => [1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,8),(9,10),(11,12)] => 12
[1,1,1,0,0,1,0,1,1,0,0,0] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,8),(9,12),(10,11)] => 13
[1,1,1,0,0,1,1,0,0,0,1,0] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,6),(4,5),(7,10),(8,9),(12,13)] => 12
[1,1,1,0,0,1,1,0,0,1,0,0] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,10),(8,9),(11,12)] => 13
[1,1,1,0,0,1,1,0,1,0,0,0] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,12),(8,9),(10,11)] => 14
[1,1,1,0,0,1,1,1,0,0,0,0] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,6),(4,5),(7,12),(8,11),(9,10)] => 15
[1,1,1,0,1,0,0,0,1,0,1,0] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,8),(4,5),(6,7),(10,11),(12,13)] => 11
[1,1,1,0,1,0,0,0,1,1,0,0] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,8),(4,5),(6,7),(10,13),(11,12)] => 12
[1,1,1,0,1,0,0,1,0,0,1,0] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,8),(4,5),(6,7),(9,10),(12,13)] => 12
[1,1,1,0,1,0,0,1,0,1,0,0] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,8),(4,5),(6,7),(9,10),(11,12)] => 13
[1,1,1,0,1,0,0,1,1,0,0,0] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,8),(4,5),(6,7),(9,12),(10,11)] => 14
[1,1,1,0,1,0,1,0,0,0,1,0] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,5),(6,7),(8,9),(12,13)] => 13
[1,1,1,0,1,0,1,0,0,1,0,0] => [1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,5),(6,7),(8,9),(11,12)] => 14
[1,1,1,0,1,0,1,0,1,0,0,0] => [1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,7),(8,9),(10,11)] => 15
[1,1,1,0,1,0,1,1,0,0,0,0] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,7),(8,11),(9,10)] => 16
[1,1,1,0,1,1,0,0,0,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,5),(6,9),(7,8),(12,13)] => 14
[1,1,1,0,1,1,0,0,0,1,0,0] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,5),(6,9),(7,8),(11,12)] => 15
[1,1,1,0,1,1,0,0,1,0,0,0] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,9),(7,8),(10,11)] => 16
[1,1,1,0,1,1,0,1,0,0,0,0] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,8),(9,10)] => 17
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,5),(6,11),(7,10),(8,9)] => 18
[1,1,1,1,0,0,0,0,1,0,1,0] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [(1,14),(2,9),(3,8),(4,7),(5,6),(10,11),(12,13)] => 12
[1,1,1,1,0,0,0,0,1,1,0,0] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [(1,14),(2,9),(3,8),(4,7),(5,6),(10,13),(11,12)] => 13
[1,1,1,1,0,0,0,1,0,0,1,0] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [(1,14),(2,11),(3,8),(4,7),(5,6),(9,10),(12,13)] => 13
[1,1,1,1,0,0,0,1,0,1,0,0] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [(1,14),(2,13),(3,8),(4,7),(5,6),(9,10),(11,12)] => 14
[1,1,1,1,0,0,0,1,1,0,0,0] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [(1,14),(2,13),(3,8),(4,7),(5,6),(9,12),(10,11)] => 15
[1,1,1,1,0,0,1,0,0,0,1,0] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,7),(5,6),(8,9),(12,13)] => 14
[1,1,1,1,0,0,1,0,0,1,0,0] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,7),(5,6),(8,9),(11,12)] => 15
[1,1,1,1,0,0,1,0,1,0,0,0] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,7),(5,6),(8,9),(10,11)] => 16
[1,1,1,1,0,0,1,1,0,0,0,0] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,7),(5,6),(8,11),(9,10)] => 17
[1,1,1,1,0,1,0,0,0,0,1,0] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,9),(5,6),(7,8),(12,13)] => 15
[1,1,1,1,0,1,0,0,0,1,0,0] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,9),(5,6),(7,8),(11,12)] => 16
[1,1,1,1,0,1,0,0,1,0,0,0] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,9),(5,6),(7,8),(10,11)] => 17
[1,1,1,1,0,1,0,1,0,0,0,0] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,8),(9,10)] => 18
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,6),(7,10),(8,9)] => 19
[1,1,1,1,1,0,0,0,0,0,1,0] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [(1,14),(2,11),(3,10),(4,9),(5,8),(6,7),(12,13)] => 16
[1,1,1,1,1,0,0,0,0,1,0,0] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [(1,14),(2,13),(3,10),(4,9),(5,8),(6,7),(11,12)] => 17
[1,1,1,1,1,0,0,0,1,0,0,0] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [(1,14),(2,13),(3,12),(4,9),(5,8),(6,7),(10,11)] => 18
[1,1,1,1,1,0,0,1,0,0,0,0] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,8),(6,7),(9,10)] => 19
[1,1,1,1,1,0,1,0,0,0,0,0] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,7),(8,9)] => 20
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [(1,14),(2,13),(3,12),(4,11),(5,10),(6,9),(7,8)] => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15)] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,7),(3,4),(5,6),(8,9),(10,11),(12,13),(14,15)] => 9
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [(1,16),(2,7),(3,6),(4,5),(8,9),(10,11),(12,13),(14,15)] => 10
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,18),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,18),(2,5),(3,4),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)] => 9
[] => [1,0] => [(1,2)] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [(1,20),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)] => 9
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Description
The number of nestings of a perfect matching.
This is the number of pairs of edges $((a,b), (c,d))$ such that $a\le c\le d\le b$. i.e., the edge $(c,d)$ is nested inside $(a,b)$.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
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.