Identifier
Values
[1,0] => [2,1] => [1,1,0,0] => [[[]]] => 1
[1,0,1,0] => [3,1,2] => [1,1,1,0,0,0] => [[[[]]]] => 1
[1,1,0,0] => [2,3,1] => [1,1,0,1,0,0] => [[[],[]]] => 2
[1,0,1,0,1,0] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 1
[1,0,1,1,0,0] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => [[[[]],[]]] => 2
[1,1,0,0,1,0] => [2,4,1,3] => [1,1,0,1,1,0,0,0] => [[[],[[]]]] => 2
[1,1,0,1,0,0] => [4,3,1,2] => [1,1,1,1,0,0,0,0] => [[[[[]]]]] => 1
[1,1,1,0,0,0] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => [[[],[],[]]] => 3
[1,0,1,0,1,0,1,0] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 1
[1,0,1,0,1,1,0,0] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 2
[1,0,1,1,0,0,1,0] => [3,1,5,2,4] => [1,1,1,0,0,1,1,0,0,0] => [[[[]],[[]]]] => 2
[1,0,1,1,0,1,0,0] => [5,1,4,2,3] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 1
[1,0,1,1,1,0,0,0] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => [[[[]],[],[]]] => 3
[1,1,0,0,1,0,1,0] => [2,5,1,3,4] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 2
[1,1,0,0,1,1,0,0] => [2,4,1,5,3] => [1,1,0,1,1,0,0,1,0,0] => [[[],[[]],[]]] => 3
[1,1,0,1,0,0,1,0] => [5,3,1,2,4] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 1
[1,1,0,1,0,1,0,0] => [5,4,1,2,3] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 1
[1,1,0,1,1,0,0,0] => [4,3,1,5,2] => [1,1,1,1,0,0,0,1,0,0] => [[[[[]]],[]]] => 2
[1,1,1,0,0,0,1,0] => [2,3,5,1,4] => [1,1,0,1,0,1,1,0,0,0] => [[[],[],[[]]]] => 3
[1,1,1,0,0,1,0,0] => [2,5,4,1,3] => [1,1,0,1,1,1,0,0,0,0] => [[[],[[[]]]]] => 2
[1,1,1,0,1,0,0,0] => [5,3,4,1,2] => [1,1,1,1,1,0,0,0,0,0] => [[[[[[]]]]]] => 1
[1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => [[[],[],[],[]]] => 4
[1,0,1,0,1,0,1,0,1,0] => [6,1,2,3,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,0,1,0,1,0,1,1,0,0] => [5,1,2,3,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 2
[1,0,1,0,1,1,0,0,1,0] => [4,1,2,6,3,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 2
[1,0,1,0,1,1,0,1,0,0] => [6,1,2,5,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,0,1,0,1,1,1,0,0,0] => [4,1,2,5,6,3] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => 3
[1,0,1,1,0,0,1,0,1,0] => [3,1,6,2,4,5] => [1,1,1,0,0,1,1,1,0,0,0,0] => [[[[]],[[[]]]]] => 2
[1,0,1,1,0,0,1,1,0,0] => [3,1,5,2,6,4] => [1,1,1,0,0,1,1,0,0,1,0,0] => [[[[]],[[]],[]]] => 3
[1,0,1,1,0,1,0,0,1,0] => [6,1,4,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,0,1,1,0,1,0,1,0,0] => [6,1,5,2,3,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,0,1,1,0,1,1,0,0,0] => [5,1,4,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 2
[1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,2,5] => [1,1,1,0,0,1,0,1,1,0,0,0] => [[[[]],[],[[]]]] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,6,5,2,4] => [1,1,1,0,0,1,1,1,0,0,0,0] => [[[[]],[[[]]]]] => 2
[1,0,1,1,1,0,1,0,0,0] => [6,1,4,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,0,1,1,1,1,0,0,0,0] => [3,1,4,5,6,2] => [1,1,1,0,0,1,0,1,0,1,0,0] => [[[[]],[],[],[]]] => 4
[1,1,0,0,1,0,1,0,1,0] => [2,6,1,3,4,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => 2
[1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[],[[[]]],[]]] => 3
[1,1,0,0,1,1,0,0,1,0] => [2,4,1,6,3,5] => [1,1,0,1,1,0,0,1,1,0,0,0] => [[[],[[]],[[]]]] => 3
[1,1,0,0,1,1,0,1,0,0] => [2,6,1,5,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => 2
[1,1,0,0,1,1,1,0,0,0] => [2,4,1,5,6,3] => [1,1,0,1,1,0,0,1,0,1,0,0] => [[[],[[]],[],[]]] => 4
[1,1,0,1,0,0,1,0,1,0] => [6,3,1,2,4,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,0,1,0,0,1,1,0,0] => [5,3,1,2,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 2
[1,1,0,1,0,1,0,0,1,0] => [6,4,1,2,3,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,0,1,0,1,0,1,0,0] => [5,6,1,2,3,4] => [1,1,1,1,1,0,1,0,0,0,0,0] => [[[[[[],[]]]]]] => 2
[1,1,0,1,0,1,1,0,0,0] => [5,4,1,2,6,3] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 2
[1,1,0,1,1,0,0,0,1,0] => [4,3,1,6,2,5] => [1,1,1,1,0,0,0,1,1,0,0,0] => [[[[[]]],[[]]]] => 2
[1,1,0,1,1,0,0,1,0,0] => [6,3,1,5,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,0,1,1,0,1,0,0,0] => [6,4,1,5,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,0,1,1,1,0,0,0,0] => [4,3,1,5,6,2] => [1,1,1,1,0,0,0,1,0,1,0,0] => [[[[[]]],[],[]]] => 3
[1,1,1,0,0,0,1,0,1,0] => [2,3,6,1,4,5] => [1,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[[[]]]]] => 3
[1,1,1,0,0,0,1,1,0,0] => [2,3,5,1,6,4] => [1,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[[]],[]]] => 4
[1,1,1,0,0,1,0,0,1,0] => [2,6,4,1,3,5] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => 2
[1,1,1,0,0,1,0,1,0,0] => [2,6,5,1,3,4] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => 2
[1,1,1,0,0,1,1,0,0,0] => [2,5,4,1,6,3] => [1,1,0,1,1,1,0,0,0,1,0,0] => [[[],[[[]]],[]]] => 3
[1,1,1,0,1,0,0,0,1,0] => [6,3,4,1,2,5] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,1,0,1,0,0,1,0,0] => [6,3,5,1,2,4] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,1,0,1,1,0,0,0,0] => [5,3,4,1,6,2] => [1,1,1,1,1,0,0,0,0,1,0,0] => [[[[[[]]]],[]]] => 2
[1,1,1,1,0,0,0,0,1,0] => [2,3,4,6,1,5] => [1,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[[]]]] => 4
[1,1,1,1,0,0,0,1,0,0] => [2,3,6,5,1,4] => [1,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[[[]]]]] => 3
[1,1,1,1,0,0,1,0,0,0] => [2,6,4,5,1,3] => [1,1,0,1,1,1,1,0,0,0,0,0] => [[[],[[[[]]]]]] => 2
[1,1,1,1,0,1,0,0,0,0] => [6,3,4,5,1,2] => [1,1,1,1,1,1,0,0,0,0,0,0] => [[[[[[[]]]]]]] => 1
[1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [1,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[]]] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => [7,1,2,3,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,0,1,0,1,0,1,1,0,0] => [6,1,2,3,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,0,1,0,1,0,1,1,0,0,1,0] => [5,1,2,3,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[[]]]],[[]]]] => 2
[1,0,1,0,1,0,1,1,0,1,0,0] => [7,1,2,3,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,0,1,0,1,1,1,0,0,0] => [5,1,2,3,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[[]]]],[],[]]] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => [4,1,2,7,3,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[[]]],[[[]]]]] => 2
[1,0,1,0,1,1,0,0,1,1,0,0] => [4,1,2,6,3,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[[]]],[[]],[]]] => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => [7,1,2,5,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,0,1,1,0,1,0,1,0,0] => [7,1,2,6,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,0,1,1,0,1,1,0,0,0] => [6,1,2,5,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[[]]],[],[[]]]] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => [4,1,2,7,6,3,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[[]]],[[[]]]]] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => [7,1,2,5,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [4,1,2,5,6,7,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[]]] => 4
[1,0,1,1,0,0,1,0,1,0,1,0] => [3,1,7,2,4,5,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[]],[[[[]]]]]] => 2
[1,0,1,1,0,0,1,0,1,1,0,0] => [3,1,6,2,4,7,5] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[]],[[[]]],[]]] => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => [3,1,5,2,7,4,6] => [1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[[[]],[[]],[[]]]] => 3
[1,0,1,1,0,0,1,1,0,1,0,0] => [3,1,7,2,6,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[]],[[[[]]]]]] => 2
[1,0,1,1,0,0,1,1,1,0,0,0] => [3,1,5,2,6,7,4] => [1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[[[]],[[]],[],[]]] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => [7,1,4,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,0,1,0,0,1,1,0,0] => [6,1,4,2,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,0,1,1,0,1,0,1,0,0,1,0] => [7,1,5,2,3,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,0,1,0,1,0,1,0,0] => [6,1,7,2,3,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[[[[]],[]]]]]] => 2
[1,0,1,1,0,1,0,1,1,0,0,0] => [6,1,5,2,3,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => [5,1,4,2,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[[]]]],[[]]]] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => [7,1,4,2,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => [7,1,5,2,6,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => [5,1,4,2,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[[]]]],[],[]]] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,7,2,5,6] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[[]],[],[[[]]]]] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => [3,1,4,6,2,7,5] => [1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[[[]],[],[[]],[]]] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => [3,1,7,5,2,4,6] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[]],[[[[]]]]]] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => [3,1,7,6,2,4,5] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[]],[[[[]]]]]] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,1,6,5,2,7,4] => [1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[[[]],[[[]]],[]]] => 3
[1,0,1,1,1,0,1,0,0,0,1,0] => [7,1,4,5,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [7,1,4,6,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [7,1,6,5,2,3,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [6,1,4,5,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
>>> Load all 204 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,7,2,6] => [1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[[[]],[],[],[[]]]] => 4
[1,0,1,1,1,1,0,0,0,1,0,0] => [3,1,4,7,6,2,5] => [1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[[[]],[],[[[]]]]] => 3
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,7,5,6,2,4] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[[[]],[[[[]]]]]] => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => [7,1,4,5,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [3,1,4,5,6,7,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[]]] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [2,7,1,3,4,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,0,0,1,0,1,0,1,1,0,0] => [2,6,1,3,4,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => 3
[1,1,0,0,1,0,1,1,0,0,1,0] => [2,5,1,3,7,4,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[[],[[[]]],[[]]]] => 3
[1,1,0,0,1,0,1,1,0,1,0,0] => [2,7,1,3,6,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,1,3,6,7,4] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[],[[[]]],[],[]]] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => [2,4,1,7,3,5,6] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[[],[[]],[[[]]]]] => 3
[1,1,0,0,1,1,0,0,1,1,0,0] => [2,4,1,6,3,7,5] => [1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[[],[[]],[[]],[]]] => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => [2,7,1,5,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,0,0,1,1,0,1,0,1,0,0] => [2,7,1,6,3,4,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,0,0,1,1,0,1,1,0,0,0] => [2,6,1,5,3,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => [2,4,1,5,7,3,6] => [1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[[],[[]],[],[[]]]] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => [2,4,1,7,6,3,5] => [1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[[],[[]],[[[]]]]] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [2,7,1,5,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,4,1,5,6,7,3] => [1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[[],[[]],[],[],[]]] => 5
[1,1,0,1,0,0,1,0,1,0,1,0] => [7,3,1,2,4,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => [6,3,1,2,4,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,0,1,0,0,1,1,0,0,1,0] => [5,3,1,2,7,4,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[[]]]],[[]]]] => 2
[1,1,0,1,0,0,1,1,0,1,0,0] => [7,3,1,2,6,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,0,0,1,1,1,0,0,0] => [5,3,1,2,6,7,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[[]]]],[],[]]] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => [7,4,1,2,3,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => [6,4,1,2,3,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,0,1,0,1,0,1,0,0,1,0] => [5,7,1,2,3,4,6] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[[[],[[]]]]]]] => 2
[1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,1,2,3,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,1,2,3,7,4] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[[[[[],[]]]],[]]] => 3
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,4,1,2,7,3,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[[]]]],[[]]]] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [7,4,1,2,6,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [5,7,1,2,6,3,4] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[[[[[],[[]]]]]]] => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [5,4,1,2,6,7,3] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[[]]]],[],[]]] => 3
[1,1,0,1,1,0,0,0,1,0,1,0] => [4,3,1,7,2,5,6] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[[]]],[[[]]]]] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,3,1,6,2,7,5] => [1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[[[[]]],[[]],[]]] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => [7,3,1,5,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => [7,3,1,6,2,4,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => [6,3,1,5,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,1,5,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [7,4,1,6,2,3,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [6,7,1,5,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[[],[]]]]]]] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => [6,4,1,5,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,0,1,1,1,0,0,0,0,1,0] => [4,3,1,5,7,2,6] => [1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[[[[]]],[],[[]]]] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,3,1,7,6,2,5] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[[[[]]],[[[]]]]] => 2
[1,1,0,1,1,1,0,0,1,0,0,0] => [7,3,1,5,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [7,4,1,5,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [4,3,1,5,6,7,2] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[]]] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [2,3,7,1,4,5,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[[],[],[[[[]]]]]] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => [2,3,6,1,4,7,5] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[[],[],[[[]]],[]]] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => [2,3,5,1,7,4,6] => [1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[[],[],[[]],[[]]]] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [2,3,7,1,6,4,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[[],[],[[[[]]]]]] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => [2,3,5,1,6,7,4] => [1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[[],[],[[]],[],[]]] => 5
[1,1,1,0,0,1,0,0,1,0,1,0] => [2,7,4,1,3,5,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,4,1,3,7,5] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [2,7,5,1,3,4,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => [2,6,7,1,3,4,5] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[[],[[[[],[]]]]]] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => [2,6,5,1,3,7,4] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => 3
[1,1,1,0,0,1,1,0,0,0,1,0] => [2,5,4,1,7,3,6] => [1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[[],[[[]]],[[]]]] => 3
[1,1,1,0,0,1,1,0,0,1,0,0] => [2,7,4,1,6,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [2,7,5,1,6,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,5,4,1,6,7,3] => [1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[[],[[[]]],[],[]]] => 4
[1,1,1,0,1,0,0,0,1,0,1,0] => [7,3,4,1,2,5,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => [6,3,4,1,2,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [7,3,5,1,2,4,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => [6,3,7,1,2,4,5] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[[[[[[]],[]]]]]] => 2
[1,1,1,0,1,0,0,1,1,0,0,0] => [6,3,5,1,2,7,4] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,1,0,1,0,1,0,0,0,1,0] => [7,5,4,1,2,3,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [6,7,4,1,2,3,5] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[[],[]]]]]]] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => [6,7,5,1,2,3,4] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[[[[[[],[]]]]]]] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => [6,5,4,1,2,7,3] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,3,4,1,7,2,6] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[[[[[]]]],[[]]]] => 2
[1,1,1,0,1,1,0,0,0,1,0,0] => [7,3,4,1,6,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [7,3,5,1,6,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,0,1,1,0,1,0,0,0,0] => [7,5,4,1,6,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => [5,3,4,1,6,7,2] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[[[[[]]]],[],[]]] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [2,3,4,7,1,5,6] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[],[[[]]]]] => 4
[1,1,1,1,0,0,0,0,1,1,0,0] => [2,3,4,6,1,7,5] => [1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[[],[],[],[[]],[]]] => 5
[1,1,1,1,0,0,0,1,0,0,1,0] => [2,3,7,5,1,4,6] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[[],[],[[[[]]]]]] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,7,6,1,4,5] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[[],[],[[[[]]]]]] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,6,5,1,7,4] => [1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[[],[],[[[]]],[]]] => 4
[1,1,1,1,0,0,1,0,0,0,1,0] => [2,7,4,5,1,3,6] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,1,0,0,1,0,0,1,0,0] => [2,7,4,6,1,3,5] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,1,0,0,1,0,1,0,0,0] => [2,7,6,5,1,3,4] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,6,4,5,1,7,3] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[[],[[[[]]]],[]]] => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [7,3,4,6,1,2,5] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [7,3,6,5,1,2,4] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => [7,6,4,5,1,2,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => [6,3,4,5,1,7,2] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[[[[[[]]]]],[]]] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [2,3,4,5,7,1,6] => [1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[[],[],[],[],[[]]]] => 5
[1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,4,7,6,1,5] => [1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[[],[],[],[[[]]]]] => 4
[1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,7,5,6,1,4] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[[],[],[[[[]]]]]] => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => [2,7,4,5,6,1,3] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[[],[[[[[]]]]]]] => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => [7,3,4,5,6,1,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[[[[[[[]]]]]]]] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[]]] => 6
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,1,2,5,6,7,8,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[],[]]] => 5
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,1,4,5,6,7,8,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[],[]]] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [4,3,1,5,6,7,8,2] => [1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[[[[]]],[],[],[],[]]] => 5
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[],[]]] => 7
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,1,4,5,6,7,8,9,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[[]],[],[],[],[],[],[]]] => 7
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[],[],[]]] => 8
[] => [1] => [1,0] => [[]] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[[],[],[],[],[],[],[],[],[]]] => 9
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Description
The number of leaves of an ordered tree.
This is the number of nodes which do not have any children.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
Ringel
Description
The Ringel permutation of the LNakayama algebra corresponding to a Dyck path.
Map
to ordered tree
Description
Sends a Dyck path to the ordered tree encoding the heights of the path.
This map is recursively defined as follows: A Dyck path $D$ of semilength $n$ may be decomposed, according to its returns (St000011The number of touch points (or returns) of a Dyck path.), into smaller paths $D_1,\dots,D_k$ of respective semilengths $n_1,\dots,n_k$ (so one has $n = n_1 + \dots n_k$) each of which has no returns.
Denote by $\tilde D_i$ the path of semilength $n_i-1$ obtained from $D_i$ by removing the initial up- and the final down-step.
This map then sends $D$ to the tree $T$ having a root note with ordered children $T_1,\dots,T_k$ which are again ordered trees computed from $D_1,\dots,D_k$ respectively.
The unique path of semilength $1$ is sent to the tree consisting of a single node.