Identifier
Values
[(1,2)] => [2,1] => [1,2] => [1,0,1,0] => 1
[(1,2),(3,4)] => [2,1,4,3] => [3,4,1,2] => [1,1,1,0,1,0,0,0] => 3
[(1,3),(2,4)] => [3,4,1,2] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 2
[(1,4),(2,3)] => [3,4,2,1] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 2
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [5,6,3,4,1,2] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [5,6,2,1,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[(1,4),(2,3),(5,6)] => [3,4,2,1,6,5] => [5,6,1,2,4,3] => [1,1,1,1,1,0,1,0,0,0,0,0] => 5
[(1,5),(2,3),(4,6)] => [3,5,2,6,1,4] => [4,1,6,2,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
[(1,6),(2,3),(4,5)] => [3,5,2,6,4,1] => [1,4,6,2,5,3] => [1,0,1,1,1,0,1,1,0,0,0,0] => 4
[(1,6),(2,4),(3,5)] => [4,5,6,2,3,1] => [1,3,2,6,5,4] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
[(1,5),(2,4),(3,6)] => [4,5,6,2,1,3] => [3,1,2,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [3,2,1,6,5,4] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [4,2,6,1,5,3] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [4,3,6,5,1,2] => [1,1,1,1,0,0,1,1,0,0,0,0] => 4
[(1,2),(3,6),(4,5)] => [2,1,5,6,4,3] => [3,4,6,5,1,2] => [1,1,1,0,1,0,1,1,0,0,0,0] => 4
[(1,3),(2,6),(4,5)] => [3,5,1,6,4,2] => [2,4,6,1,5,3] => [1,1,0,1,1,0,1,1,0,0,0,0] => 4
[(1,4),(2,6),(3,5)] => [4,5,6,1,3,2] => [2,3,1,6,5,4] => [1,1,0,1,0,0,1,1,1,0,0,0] => 3
[(1,5),(2,6),(3,4)] => [4,5,6,3,1,2] => [2,1,3,6,5,4] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
[(1,6),(2,5),(3,4)] => [4,5,6,3,2,1] => [1,2,3,6,5,4] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [7,8,5,6,2,1,4,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,4),(2,3),(5,6),(7,8)] => [3,4,2,1,6,5,8,7] => [7,8,5,6,1,2,4,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,5),(2,3),(4,6),(7,8)] => [3,5,2,6,1,4,8,7] => [7,8,4,1,6,2,5,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,6),(2,3),(4,5),(7,8)] => [3,5,2,6,4,1,8,7] => [7,8,1,4,6,2,5,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,7),(2,3),(4,5),(6,8)] => [3,5,2,7,4,8,1,6] => [6,1,8,4,7,2,5,3] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,8),(2,3),(4,5),(6,7)] => [3,5,2,7,4,8,6,1] => [1,6,8,4,7,2,5,3] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,8),(2,4),(3,5),(6,7)] => [4,5,7,2,3,8,6,1] => [1,6,8,3,2,7,5,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,7),(2,4),(3,5),(6,8)] => [4,5,7,2,3,8,1,6] => [6,1,8,3,2,7,5,4] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,6),(2,4),(3,5),(7,8)] => [4,5,6,2,3,1,8,7] => [7,8,1,3,2,6,5,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,5),(2,4),(3,6),(7,8)] => [4,5,6,2,1,3,8,7] => [7,8,3,1,2,6,5,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [7,8,3,2,1,6,5,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [7,8,4,2,6,1,5,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [7,8,4,3,6,5,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,2),(3,6),(4,5),(7,8)] => [2,1,5,6,4,3,8,7] => [7,8,3,4,6,5,1,2] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,3),(2,6),(4,5),(7,8)] => [3,5,1,6,4,2,8,7] => [7,8,2,4,6,1,5,3] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,4),(2,6),(3,5),(7,8)] => [4,5,6,1,3,2,8,7] => [7,8,2,3,1,6,5,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,5),(2,6),(3,4),(7,8)] => [4,5,6,3,1,2,8,7] => [7,8,2,1,3,6,5,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,6),(2,5),(3,4),(7,8)] => [4,5,6,3,2,1,8,7] => [7,8,1,2,3,6,5,4] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => 7
[(1,7),(2,5),(3,4),(6,8)] => [4,5,7,3,2,8,1,6] => [6,1,8,2,3,7,5,4] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,8),(2,5),(3,4),(6,7)] => [4,5,7,3,2,8,6,1] => [1,6,8,2,3,7,5,4] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,7),(2,6),(3,4),(5,8)] => [4,6,7,3,8,2,1,5] => [5,1,2,8,3,7,6,4] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,6),(2,7),(3,4),(5,8)] => [4,6,7,3,8,1,2,5] => [5,2,1,8,3,7,6,4] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,5),(2,7),(3,4),(6,8)] => [4,5,7,3,1,8,2,6] => [6,2,8,1,3,7,5,4] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,4),(2,7),(3,5),(6,8)] => [4,5,7,1,3,8,2,6] => [6,2,8,3,1,7,5,4] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,3),(2,7),(4,5),(6,8)] => [3,5,1,7,4,8,2,6] => [6,2,8,4,7,1,5,3] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,2),(3,7),(4,5),(6,8)] => [2,1,5,7,4,8,3,6] => [6,3,8,4,7,5,1,2] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,2),(3,8),(4,5),(6,7)] => [2,1,5,7,4,8,6,3] => [3,6,8,4,7,5,1,2] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,3),(2,8),(4,5),(6,7)] => [3,5,1,7,4,8,6,2] => [2,6,8,4,7,1,5,3] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,4),(2,8),(3,5),(6,7)] => [4,5,7,1,3,8,6,2] => [2,6,8,3,1,7,5,4] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,5),(2,8),(3,4),(6,7)] => [4,5,7,3,1,8,6,2] => [2,6,8,1,3,7,5,4] => [1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,7),(2,8),(3,4),(5,6)] => [4,6,7,3,8,5,1,2] => [2,1,5,8,3,7,6,4] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 5
[(1,8),(2,7),(3,5),(4,6)] => [5,6,7,8,3,4,2,1] => [1,2,4,3,8,7,6,5] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[(1,7),(2,8),(3,5),(4,6)] => [5,6,7,8,3,4,1,2] => [2,1,4,3,8,7,6,5] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
[(1,2),(3,8),(4,6),(5,7)] => [2,1,6,7,8,4,5,3] => [3,5,4,8,7,6,1,2] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[(1,2),(3,7),(4,6),(5,8)] => [2,1,6,7,8,4,3,5] => [5,3,4,8,7,6,1,2] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,3),(2,7),(4,6),(5,8)] => [3,6,1,7,8,4,2,5] => [5,2,4,8,7,1,6,3] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,4),(2,7),(3,6),(5,8)] => [4,6,7,1,8,3,2,5] => [5,2,3,8,1,7,6,4] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,5),(2,7),(3,6),(4,8)] => [5,6,7,8,1,3,2,4] => [4,2,3,1,8,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,6),(2,7),(3,5),(4,8)] => [5,6,7,8,3,1,2,4] => [4,2,1,3,8,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,7),(2,6),(3,5),(4,8)] => [5,6,7,8,3,2,1,4] => [4,1,2,3,8,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,8),(2,6),(3,5),(4,7)] => [5,6,7,8,3,2,4,1] => [1,4,2,3,8,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,8),(2,5),(3,6),(4,7)] => [5,6,7,8,2,3,4,1] => [1,4,3,2,8,7,6,5] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,7),(2,5),(3,6),(4,8)] => [5,6,7,8,2,3,1,4] => [4,1,3,2,8,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,6),(2,5),(3,7),(4,8)] => [5,6,7,8,2,1,3,4] => [4,3,1,2,8,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [4,3,2,1,8,7,6,5] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [5,3,2,8,1,7,6,4] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [5,4,2,8,7,1,6,3] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [5,4,3,8,7,6,1,2] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [6,4,8,3,7,5,1,2] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [6,4,8,2,7,1,5,3] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [6,3,8,2,1,7,5,4] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,5),(2,4),(3,7),(6,8)] => [4,5,7,2,1,8,3,6] => [6,3,8,1,2,7,5,4] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,6),(2,4),(3,7),(5,8)] => [4,6,7,2,8,1,3,5] => [5,3,1,8,2,7,6,4] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,7),(2,4),(3,6),(5,8)] => [4,6,7,2,8,3,1,5] => [5,1,3,8,2,7,6,4] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,7),(2,3),(4,6),(5,8)] => [3,6,2,7,8,4,1,5] => [5,1,4,8,7,2,6,3] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,6),(2,3),(4,7),(5,8)] => [3,6,2,7,8,1,4,5] => [5,4,1,8,7,2,6,3] => [1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => 5
[(1,5),(2,3),(4,7),(6,8)] => [3,5,2,7,1,8,4,6] => [6,4,8,1,7,2,5,3] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,4),(2,3),(5,7),(6,8)] => [3,4,2,1,7,8,5,6] => [6,5,8,7,1,2,4,3] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [6,5,8,7,2,1,4,3] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [6,5,8,7,3,4,1,2] => [1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => 6
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,7,8,6,5] => [5,6,8,7,3,4,1,2] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 6
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,7,8,6,5] => [5,6,8,7,2,1,4,3] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 6
[(1,4),(2,3),(5,8),(6,7)] => [3,4,2,1,7,8,6,5] => [5,6,8,7,1,2,4,3] => [1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => 6
[(1,5),(2,3),(4,8),(6,7)] => [3,5,2,7,1,8,6,4] => [4,6,8,1,7,2,5,3] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,6),(2,3),(4,8),(5,7)] => [3,6,2,7,8,1,5,4] => [4,5,1,8,7,2,6,3] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 5
[(1,7),(2,3),(4,8),(5,6)] => [3,6,2,7,8,5,1,4] => [4,1,5,8,7,2,6,3] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 5
[(1,8),(2,3),(4,7),(5,6)] => [3,6,2,7,8,5,4,1] => [1,4,5,8,7,2,6,3] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 5
[(1,6),(2,4),(3,8),(5,7)] => [4,6,7,2,8,1,5,3] => [3,5,1,8,2,7,6,4] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[(1,5),(2,4),(3,8),(6,7)] => [4,5,7,2,1,8,6,3] => [3,6,8,1,2,7,5,4] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,4),(2,5),(3,8),(6,7)] => [4,5,7,1,2,8,6,3] => [3,6,8,2,1,7,5,4] => [1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,7,2,8,6,4] => [4,6,8,2,7,1,5,3] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,7,3,8,6,4] => [4,6,8,3,7,5,1,2] => [1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => 6
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,7,8,3,5,4] => [4,5,3,8,7,6,1,2] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 5
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,7,8,2,5,4] => [4,5,2,8,7,1,6,3] => [1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => 5
[(1,4),(2,6),(3,8),(5,7)] => [4,6,7,1,8,2,5,3] => [3,5,2,8,1,7,6,4] => [1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0] => 5
[(1,5),(2,6),(3,8),(4,7)] => [5,6,7,8,1,2,4,3] => [3,4,2,1,8,7,6,5] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,6),(2,5),(3,8),(4,7)] => [5,6,7,8,2,1,4,3] => [3,4,1,2,8,7,6,5] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => 4
[(1,7),(2,5),(3,8),(4,6)] => [5,6,7,8,2,4,1,3] => [3,1,4,2,8,7,6,5] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[(1,8),(2,5),(3,7),(4,6)] => [5,6,7,8,2,4,3,1] => [1,3,4,2,8,7,6,5] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[(1,8),(2,6),(3,7),(4,5)] => [5,6,7,8,4,2,3,1] => [1,3,2,4,8,7,6,5] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[(1,5),(2,7),(3,8),(4,6)] => [5,6,7,8,1,4,2,3] => [3,2,4,1,8,7,6,5] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => 4
>>> Load all 128 entries. <<<
[(1,3),(2,7),(4,8),(5,6)] => [3,6,1,7,8,5,2,4] => [4,2,5,8,7,1,6,3] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 5
[(1,2),(3,7),(4,8),(5,6)] => [2,1,6,7,8,5,3,4] => [4,3,5,8,7,6,1,2] => [1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0] => 5
[(1,2),(3,8),(4,7),(5,6)] => [2,1,6,7,8,5,4,3] => [3,4,5,8,7,6,1,2] => [1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => 5
[(1,5),(2,8),(3,7),(4,6)] => [5,6,7,8,1,4,3,2] => [2,3,4,1,8,7,6,5] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => 4
[(1,6),(2,8),(3,7),(4,5)] => [5,6,7,8,4,1,3,2] => [2,3,1,4,8,7,6,5] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
[(1,7),(2,8),(3,6),(4,5)] => [5,6,7,8,4,3,1,2] => [2,1,3,4,8,7,6,5] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[(1,8),(2,7),(3,6),(4,5)] => [5,6,7,8,4,3,2,1] => [1,2,3,4,8,7,6,5] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [9,10,7,8,5,6,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [3,4,2,1,6,5,8,7,10,9] => [9,10,7,8,5,6,1,2,4,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [3,5,2,6,4,1,8,7,10,9] => [9,10,7,8,1,4,6,2,5,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [3,5,2,7,4,8,6,1,10,9] => [9,10,1,6,8,4,7,2,5,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,5,6,4,3,8,7,10,9] => [9,10,7,8,3,4,6,5,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [4,5,6,3,2,1,8,7,10,9] => [9,10,7,8,1,2,3,6,5,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [4,5,7,3,2,8,6,1,10,9] => [9,10,1,6,8,2,3,7,5,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,5,7,4,8,6,3,10,9] => [9,10,3,6,8,4,7,5,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [4,6,7,3,8,5,2,1,10,9] => [9,10,1,2,5,8,3,7,6,4] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,7,8,6,5,10,9] => [9,10,5,6,8,7,3,4,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [3,4,2,1,7,8,6,5,10,9] => [9,10,5,6,8,7,1,2,4,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [3,6,2,7,8,5,4,1,10,9] => [9,10,1,4,5,8,7,2,6,3] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,6,7,8,5,4,3,10,9] => [9,10,3,4,5,8,7,6,1,2] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [5,6,7,8,4,3,2,1,10,9] => [9,10,1,2,3,4,8,7,6,5] => [1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => 9
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [5,4,3,2,1,10,9,8,7,6] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,9,10,8,7] => [7,8,10,9,5,6,3,4,1,2] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [3,4,2,1,6,5,9,10,8,7] => [7,8,10,9,5,6,1,2,4,3] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [3,5,2,6,4,1,9,10,8,7] => [7,8,10,9,1,4,6,2,5,3] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,5,6,4,3,9,10,8,7] => [7,8,10,9,3,4,6,5,1,2] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 8
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [4,5,6,3,2,1,9,10,8,7] => [7,8,10,9,1,2,3,6,5,4] => [1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => 8
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Description
The height of a Dyck path.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
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
non-nesting-exceedence permutation
Description
The fixed-point-free permutation with deficiencies given by the perfect matching, no alignments and no inversions between exceedences.
Put differently, the exceedences form the unique non-nesting perfect matching whose openers coincide with those of the given perfect matching.