Identifier
Values
[(1,2)] => [2,1] => [2,1] => [2,1] => 0
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => [2,1,4,3] => 0
[(1,3),(2,4)] => [3,4,1,2] => [3,1,4,2] => [3,1,4,2] => 0
[(1,4),(2,3)] => [4,3,2,1] => [3,2,4,1] => [3,2,4,1] => 0
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => [2,1,6,5,4,3] => 1
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [3,1,4,2,6,5] => [3,1,6,5,4,2] => 1
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [3,2,4,1,6,5] => [3,2,6,1,5,4] => 0
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [3,2,5,1,6,4] => [3,2,6,1,5,4] => 0
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [3,2,5,4,6,1] => [3,2,6,5,4,1] => 1
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [4,2,5,3,6,1] => [4,2,6,5,3,1] => 1
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [4,2,5,1,6,3] => [4,2,6,1,5,3] => 0
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [4,1,5,2,6,3] => [4,1,6,5,3,2] => 1
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [3,1,5,2,6,4] => [3,1,6,5,4,2] => 1
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,5,3,6,4] => [2,1,6,5,4,3] => 1
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,5,4,6,3] => [2,1,6,5,4,3] => 1
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [3,1,5,4,6,2] => [3,1,6,5,4,2] => 1
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [4,1,5,3,6,2] => [4,1,6,5,3,2] => 1
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [4,3,5,1,6,2] => [4,3,6,1,5,2] => 0
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => [4,3,6,2,5,1] => 0
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,5,3,6,4,8,7] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,5,4,7,3,8,6] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,6,4,7,5,8,3] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,6,4,7,3,8,5] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,6,3,7,4,8,5] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,5,3,7,4,8,6] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,7,5,8,6] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,5,3,7,6,8,4] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,6,3,7,5,8,4] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,6,5,7,3,8,4] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => [2,1,8,7,6,5,4,3] => 2
[(1,2),(3,4),(5,6),(7,8),(9,10)] => [2,1,4,3,6,5,8,7,10,9] => [2,1,4,3,6,5,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,5,3,6,4,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,5,4,6,3,8,7,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,5,4,7,6,8,3,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [2,1,5,4,7,6,9,8,10,3] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,6,3,7,4,8,5,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [2,1,5,7,3,8,4,6,10,9] => [2,1,5,3,7,4,8,6,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,7,5,8,6,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,7,6,8,5,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,6,5,7,4,8,3,10,9] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,6,5,7,4,9,8,10,3] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,7,6,9,8,10,5] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,6,5,8,7,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,7,3,8,4,9,5,10,6] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [2,1,6,8,9,3,10,4,5,7] => [2,1,6,3,8,4,9,5,10,7] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [2,1,5,8,3,9,10,4,6,7] => [2,1,5,3,8,4,9,6,10,7] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,8,5,9,6,10,7] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [2,1,4,3,7,9,5,10,6,8] => [2,1,4,3,7,5,9,6,10,8] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [2,1,5,7,3,9,4,10,6,8] => [2,1,5,3,7,4,9,6,10,8] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [2,1,6,7,9,3,4,10,5,8] => [2,1,6,3,7,4,9,5,10,8] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,5,3,6,4,9,7,10,8] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,9,7,10,8] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,9,8,10,7] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,5,4,6,3,9,8,10,7] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,5,4,8,7,9,6,10,3] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,8,7,9,6,10,5] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,7,6,8,5,9,4,10,3] => [2,1,10,9,8,7,6,5,4,3] => 3
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,7,6,8,5,9,4,10,3,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,7,6,8,5,9,4,11,10,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,7,6,8,5,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,7,6,8,5,10,9,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,7,6,8,5,11,10,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,5,4,7,6,9,8,10,3,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,5,4,7,6,9,8,11,10,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,7,6,9,8,10,5,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,7,6,9,8,10,5,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,1,4,3,7,6,9,8,11,10,12,5] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,5,4,7,6,8,3,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,5,4,7,6,10,9,11,8,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,5,4,7,6,8,3,11,10,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,7,6,10,9,11,8,12,5] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,6,5,8,7,9,4,10,3,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,6,5,8,7,9,4,11,10,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12)] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,4,3,6,5,8,7,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,6,5,8,7,10,9,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,11,10,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,5,4,8,7,9,6,10,3,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,5,4,8,7,9,6,11,10,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,8,7,9,6,10,5,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,8,7,9,6,10,5,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,8,7,9,6,11,10,12,5] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,5,4,6,3,8,7,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,5,4,8,7,10,9,11,6,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,5,4,6,3,8,7,11,10,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,8,7,10,9,11,6,12,5] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,6,5,7,4,9,8,10,3,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,6,5,7,4,9,8,11,10,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,9,8,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,6,5,9,8,10,7,11,4,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,9,8,11,10,12,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,6,5,7,4,8,3,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,6,5,7,4,10,9,11,8,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,6,5,7,4,8,3,11,10,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,10,9,11,8,12,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,5,4,6,3,9,8,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,5,4,9,8,10,7,11,6,12,3] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,5,4,6,3,9,8,11,10,12,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
>>> Load all 144 entries. <<<
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,9,8,10,7,11,6,12,5] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,5,4,6,3,10,9,11,8,12,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,11,9,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,9,7,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => [2,1,4,3,6,5,9,11,7,12,8,10] => [2,1,4,3,6,5,9,7,11,8,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,10,7,11,8,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,7,5,8,6,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,7,5,8,6,11,9,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => [2,1,4,3,7,9,5,10,6,8,12,11] => [2,1,4,3,7,5,9,6,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => [2,1,4,3,7,9,5,11,6,12,8,10] => [2,1,4,3,7,5,9,6,11,8,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => [2,1,4,3,7,10,5,11,12,6,8,9] => [2,1,4,3,7,5,10,6,11,8,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,8,5,9,6,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => [2,1,4,3,8,9,11,5,6,12,7,10] => [2,1,4,3,8,5,9,6,11,7,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => [2,1,4,3,8,10,11,5,12,6,7,9] => [2,1,4,3,8,5,10,6,11,7,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,9,5,10,6,11,7,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,5,3,6,4,8,7,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,5,3,6,4,8,7,11,9,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,5,3,6,4,9,7,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => [2,1,5,6,3,4,9,11,7,12,8,10] => [2,1,5,3,6,4,9,7,11,8,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,5,3,6,4,10,7,11,8,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => [2,1,5,7,3,8,4,6,10,9,12,11] => [2,1,5,3,7,4,8,6,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => [2,1,5,7,3,8,4,6,11,12,9,10] => [2,1,5,3,7,4,8,6,11,9,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => [2,1,5,7,3,9,4,10,6,8,12,11] => [2,1,5,3,7,4,9,6,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10] => [2,1,5,3,7,4,9,6,11,8,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => [2,1,5,7,3,10,4,11,12,6,8,9] => [2,1,5,3,7,4,10,6,11,8,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => [2,1,5,8,3,9,10,4,6,7,12,11] => [2,1,5,3,8,4,9,6,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => [2,1,5,8,3,9,11,4,6,12,7,10] => [2,1,5,3,8,4,9,6,11,7,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => [2,1,5,8,3,10,11,4,12,6,7,9] => [2,1,5,3,8,4,10,6,11,7,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => [2,1,5,9,3,10,11,12,4,6,7,8] => [2,1,5,3,9,4,10,6,11,7,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,6,3,7,4,8,5,10,9,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,6,3,7,4,8,5,11,9,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => [2,1,6,7,9,3,4,10,5,8,12,11] => [2,1,6,3,7,4,9,5,10,8,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => [2,1,6,7,9,3,4,11,5,12,8,10] => [2,1,6,3,7,4,9,5,11,8,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => [2,1,6,7,10,3,4,11,12,5,8,9] => [2,1,6,3,7,4,10,5,11,8,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => [2,1,6,8,9,3,10,4,5,7,12,11] => [2,1,6,3,8,4,9,5,10,7,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => [2,1,6,8,9,3,11,4,5,12,7,10] => [2,1,6,3,8,4,9,5,11,7,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => [2,1,6,8,10,3,11,4,12,5,7,9] => [2,1,6,3,8,4,10,5,11,7,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => [2,1,6,9,10,3,11,12,4,5,7,8] => [2,1,6,3,9,4,10,5,11,7,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,7,3,8,4,9,5,10,6,12,11] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => [2,1,7,8,9,11,3,4,5,12,6,10] => [2,1,7,3,8,4,9,5,11,6,12,10] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => [2,1,7,8,10,11,3,4,12,5,6,9] => [2,1,7,3,8,4,10,5,11,6,12,9] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => [2,1,7,9,10,11,3,12,4,5,6,8] => [2,1,7,3,9,4,10,5,11,6,12,8] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,8,3,9,4,10,5,11,6,12,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => 4
search for individual values
searching the database for the individual values of this statistic
/ search for generating function
searching the database for statistics with the same generating function
Description
The number of even descents of a permutation.
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
Simion-Schmidt map
Description
The Simion-Schmidt map sends any permutation to a $123$-avoiding permutation.
Details can be found in [1].
In particular, this is a bijection between $132$-avoiding permutations and $123$-avoiding permutations, see [1, Proposition 19].
Map
inverse first fundamental transformation
Description
Let $\sigma = (i_{11}\cdots i_{1k_1})\cdots(i_{\ell 1}\cdots i_{\ell k_\ell})$ be a permutation given by cycle notation such that every cycle starts with its maximal entry, and all cycles are ordered increasingly by these maximal entries.
Maps $\sigma$ to the permutation $[i_{11},\ldots,i_{1k_1},\ldots,i_{\ell 1},\ldots,i_{\ell k_\ell}]$ in one-line notation.
In other words, this map sends the maximal entries of the cycles to the left-to-right maxima, and the sequences between two left-to-right maxima are given by the cycles.