Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00236: Permutations —Clarke-Steingrimsson-Zeng inverse⟶ Permutations
Mp00131: Permutations —descent bottoms⟶ Binary words
Images
[(1,2)] => [2,1] => [2,1] => 1
[(1,2),(3,4)] => [2,1,4,3] => [2,1,4,3] => 101
[(1,3),(2,4)] => [3,4,1,2] => [4,1,3,2] => 110
[(1,4),(2,3)] => [4,3,2,1] => [3,2,4,1] => 110
[(1,2),(3,4),(5,6)] => [2,1,4,3,6,5] => [2,1,4,3,6,5] => 10101
[(1,3),(2,4),(5,6)] => [3,4,1,2,6,5] => [4,1,3,2,6,5] => 11001
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [3,2,4,1,6,5] => 11001
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [3,2,6,1,5,4] => 11010
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [3,2,5,4,6,1] => 11010
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [5,2,4,3,6,1] => 11100
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [6,2,4,1,5,3] => 11100
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,1,5,2,4,3] => 11100
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [6,1,3,2,5,4] => 11010
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => 10110
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,5,4,6,3] => 10110
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [5,4,6,1,3,2] => 11010
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [5,1,6,3,4,2] => 11100
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [4,3,6,1,5,2] => 11100
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [4,3,5,2,6,1] => 11100
[(1,2),(3,4),(5,6),(7,8)] => [2,1,4,3,6,5,8,7] => [2,1,4,3,6,5,8,7] => 1010101
[(1,3),(2,4),(5,6),(7,8)] => [3,4,1,2,6,5,8,7] => [4,1,3,2,6,5,8,7] => 1100101
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [3,2,4,1,6,5,8,7] => 1100101
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [3,2,6,1,5,4,8,7] => 1101001
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [3,2,5,4,6,1,8,7] => 1101001
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [3,2,5,4,8,1,7,6] => 1101010
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [3,2,5,4,7,6,8,1] => 1101010
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [5,2,4,3,7,6,8,1] => 1110010
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [5,2,4,3,8,1,7,6] => 1110010
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [5,2,4,3,6,1,8,7] => 1110001
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [6,2,4,1,5,3,8,7] => 1110001
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,1,5,2,4,3,8,7] => 1110001
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [6,1,3,2,5,4,8,7] => 1101001
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => 1011001
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,5,4,6,3,8,7] => 1011001
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [5,4,6,1,3,2,8,7] => 1101001
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [5,1,6,3,4,2,8,7] => 1110001
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [4,3,6,1,5,2,8,7] => 1110001
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [4,3,5,2,6,1,8,7] => 1110001
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [4,3,5,2,8,1,7,6] => 1110010
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [4,3,5,2,7,6,8,1] => 1110010
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [4,3,7,2,6,5,8,1] => 1110100
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [4,3,8,2,6,1,7,5] => 1110100
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [4,3,8,1,7,2,6,5] => 1110100
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [4,3,8,1,5,2,7,6] => 1110010
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [5,1,8,3,4,2,7,6] => 1110010
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [5,4,8,1,3,2,7,6] => 1101010
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,5,4,8,3,7,6] => 1011010
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,5,4,7,6,8,3] => 1011010
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [5,4,7,6,8,1,3,2] => 1101010
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [5,1,7,6,8,3,4,2] => 1110010
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [4,3,7,6,8,1,5,2] => 1110010
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [4,3,7,1,8,5,6,2] => 1110100
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [4,3,6,5,8,1,7,2] => 1110100
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [4,3,6,5,7,2,8,1] => 1110100
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [6,3,5,4,7,2,8,1] => 1111000
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [6,3,5,4,8,1,7,2] => 1111000
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [7,3,5,1,8,4,6,2] => 1111000
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [7,1,6,3,8,4,5,2] => 1111000
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [7,1,6,5,8,3,4,2] => 1110100
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [7,4,6,5,8,1,3,2] => 1101100
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,7,4,6,5,8,3] => 1011100
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,8,4,6,3,7,5] => 1011100
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [8,4,6,1,3,2,7,5] => 1101100
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [8,1,6,3,4,2,7,5] => 1110100
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [8,1,6,3,7,2,5,4] => 1111000
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [8,3,5,1,7,2,6,4] => 1111000
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [8,3,5,2,6,1,7,4] => 1111000
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [7,3,5,2,6,4,8,1] => 1111000
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [7,2,6,3,5,4,8,1] => 1111000
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [8,2,6,3,5,1,7,4] => 1111000
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [8,2,7,1,5,3,6,4] => 1111000
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,1,7,2,6,3,5,4] => 1111000
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [8,1,7,2,4,3,6,5] => 1110100
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [8,1,3,2,7,4,6,5] => 1101100
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,3,7,4,6,5] => 1011100
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,8,3,5,4,7,6] => 1011010
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [8,1,3,2,5,4,7,6] => 1101010
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [8,1,5,2,4,3,7,6] => 1110010
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [8,2,4,1,5,3,7,6] => 1110010
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [8,2,4,1,7,3,6,5] => 1110100
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [8,2,4,3,6,1,7,5] => 1110100
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [7,2,4,3,6,5,8,1] => 1110100
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [3,2,7,4,6,5,8,1] => 1101100
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [3,2,8,4,6,1,7,5] => 1101100
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [3,2,8,1,7,4,6,5] => 1101100
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [3,2,8,1,5,4,7,6] => 1101010
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [3,2,4,1,8,5,7,6] => 1100110
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => 1100110
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => 1010110
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,6,8,5] => 1010110
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [4,1,3,2,7,6,8,5] => 1100110
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [3,2,4,1,7,6,8,5] => 1100110
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [3,2,7,6,8,1,5,4] => 1101010
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [3,2,7,1,8,5,6,4] => 1101100
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [3,2,6,5,8,1,7,4] => 1101100
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [3,2,6,5,7,4,8,1] => 1101100
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [6,5,7,2,4,3,8,1] => 1110100
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [6,5,8,2,4,1,7,3] => 1110100
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [7,2,4,1,8,5,6,3] => 1110100
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [7,6,8,2,4,1,5,3] => 1110010
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [7,6,8,1,5,2,4,3] => 1110010
>>> Load all 321 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [7,6,8,1,3,2,5,4] => 1101010
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,7,6,8,3,5,4] => 1011010
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,7,3,8,5,6,4] => 1011100
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [7,1,3,2,8,5,6,4] => 1101100
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [7,1,8,5,6,2,4,3] => 1110100
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [7,1,8,2,6,4,5,3] => 1111000
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [7,2,8,1,5,4,6,3] => 1111000
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [6,2,8,4,5,1,7,3] => 1111000
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [6,2,7,4,5,3,8,1] => 1111000
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [5,4,7,2,6,3,8,1] => 1111000
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [5,4,8,2,6,1,7,3] => 1111000
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [5,4,8,1,7,2,6,3] => 1111000
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [6,1,8,4,7,2,5,3] => 1111000
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [6,5,8,1,7,2,4,3] => 1110100
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [6,5,8,1,3,2,7,4] => 1101100
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,6,5,8,3,7,4] => 1011100
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,6,5,7,4,8,3] => 1011100
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [6,5,7,4,8,1,3,2] => 1101100
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [6,5,7,1,8,3,4,2] => 1110100
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [6,1,7,4,8,3,5,2] => 1111000
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [5,4,7,1,8,3,6,2] => 1111000
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [5,4,6,3,8,1,7,2] => 1111000
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [5,4,6,3,7,2,8,1] => 1111000
[(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] => 101010101
[(1,3),(2,4),(5,6),(7,8),(9,10)] => [3,4,1,2,6,5,8,7,10,9] => [4,1,3,2,6,5,8,7,10,9] => 110010101
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [3,2,4,1,6,5,8,7,10,9] => 110010101
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [3,2,5,4,6,1,8,7,10,9] => 110100101
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [3,2,5,4,7,6,8,1,10,9] => 110101001
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [3,2,5,4,7,6,9,8,10,1] => 110101010
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,3,5,4,8,7,10,9] => 101100101
[(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] => 101100101
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [4,3,5,2,6,1,8,7,10,9] => 111000101
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [4,3,5,2,7,6,8,1,10,9] => 111001001
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [4,3,5,2,7,6,9,8,10,1] => 111001010
[(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] => 101101001
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [4,3,6,5,7,2,8,1,10,9] => 111010001
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [4,3,6,5,7,2,9,8,10,1] => 111010010
[(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] => 101101010
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [4,3,6,5,8,7,9,2,10,1] => 111010100
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [4,1,3,2,8,5,7,6,10,9] => 110011001
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,8,5,7,6,10,9] => 101011001
[(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] => 101011001
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [3,2,4,1,7,6,8,5,10,9] => 110011001
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [3,2,6,5,7,4,8,1,10,9] => 110110001
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [3,2,6,5,7,4,9,8,10,1] => 110110010
[(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] => 101110001
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [5,4,6,3,7,2,8,1,10,9] => 111100001
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [5,4,6,3,7,2,9,8,10,1] => 111100010
[(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] => 101110010
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [5,4,6,3,8,7,9,2,10,1] => 111100100
[(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] => 101011010
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [3,2,4,1,7,6,9,8,10,5] => 110011010
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [3,2,6,5,8,7,9,4,10,1] => 110110100
[(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] => 101110100
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [5,4,7,6,8,3,9,2,10,1] => 111101000
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,1,9,2,8,3,7,4,6,5] => 111110000
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => [10,1,3,2,5,4,7,6,9,8] => 110101010
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,3,5,4,10,7,9,8] => 101100110
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [4,1,3,2,6,5,10,7,9,8] => 110010110
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,7,9,8] => 101010110
[(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] => 101010110
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [3,2,4,1,6,5,9,8,10,7] => 110010110
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [3,2,5,4,6,1,9,8,10,7] => 110100110
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [3,2,5,4,8,7,9,6,10,1] => 110101100
[(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] => 101100110
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [4,3,5,2,6,1,9,8,10,7] => 111000110
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [4,3,5,2,8,7,9,6,10,1] => 111001100
[(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] => 101101100
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [4,3,7,6,8,5,9,2,10,1] => 111011000
[(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] => 101011100
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [3,2,4,1,8,7,9,6,10,5] => 110011100
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [3,2,7,6,8,5,9,4,10,1] => 110111000
[(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] => 101111000
[(1,9),(2,10),(3,8),(4,7),(5,6)] => [9,10,8,7,6,5,4,3,1,2] => [6,5,7,4,8,3,10,1,9,2] => 111110000
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [6,5,7,4,8,3,9,2,10,1] => 111110000
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [7,6,8,5,9,4,10,3,11,2,12,1] => 11111100000
[(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] => 10111100001
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [3,2,7,6,8,5,9,4,11,10,12,1] => 11011100010
[(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] => 10111100010
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [3,2,7,6,8,5,9,4,10,1,12,11] => 11011100001
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [4,3,7,6,8,5,10,9,11,2,12,1] => 11101100100
[(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] => 10101100101
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [3,2,7,6,8,5,10,9,11,4,12,1] => 11011100100
[(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] => 10111100100
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [3,2,4,1,7,6,8,5,10,9,12,11] => 11001100101
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [4,3,7,6,8,5,9,2,11,10,12,1] => 11101100010
[(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] => 10101100110
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [4,3,7,6,8,5,9,2,10,1,12,11] => 11101100001
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [3,2,4,1,7,6,8,5,11,10,12,9] => 11001100110
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [5,4,7,6,9,8,10,3,11,2,12,1] => 11110101000
[(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] => 10110101001
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [3,2,5,4,7,6,9,8,11,10,12,1] => 11010101010
[(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] => 10110101010
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [3,2,5,4,7,6,9,8,10,1,12,11] => 11010101001
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [4,3,7,6,9,8,10,5,11,2,12,1] => 11101101000
[(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] => 10101101001
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [3,2,7,6,9,8,10,5,11,4,12,1] => 11011101000
[(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] => 10111101000
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [3,2,4,1,7,6,9,8,10,5,12,11] => 11001101001
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [4,3,5,2,7,6,9,8,11,10,12,1] => 11100101010
[(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] => 10101101010
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [4,3,5,2,7,6,9,8,10,1,12,11] => 11100101001
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [3,2,4,1,7,6,9,8,11,10,12,5] => 11001101010
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [5,4,7,6,8,3,10,9,11,2,12,1] => 11110100100
[(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] => 10110100101
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [3,2,5,4,7,6,10,9,11,8,12,1] => 11010101100
[(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] => 10110101100
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [3,2,5,4,7,6,8,1,10,9,12,11] => 11010100101
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [5,4,7,6,8,3,9,2,11,10,12,1] => 11110100010
[(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] => 10110100110
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [5,4,7,6,8,3,9,2,10,1,12,11] => 11110100001
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [3,2,5,4,7,6,8,1,11,10,12,9] => 11010100110
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [4,3,5,2,7,6,10,9,11,8,12,1] => 11100101100
[(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] => 10101101100
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [4,3,5,2,7,6,8,1,10,9,12,11] => 11100100101
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [3,2,4,1,7,6,10,9,11,8,12,5] => 11001101100
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [4,3,5,2,7,6,8,1,11,10,12,9] => 11100100110
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [6,5,8,7,9,4,10,3,11,2,12,1] => 11111010000
[(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] => 10111010001
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [3,2,6,5,8,7,9,4,11,10,12,1] => 11011010010
[(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] => 10111010010
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [3,2,6,5,8,7,9,4,10,1,12,11] => 11011010001
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [4,3,6,5,8,7,10,9,11,2,12,1] => 11101010100
[(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] => 10101010101
[(1,12),(2,3),(4,11),(5,6),(7,8),(9,10)] => [12,3,2,11,6,5,8,7,10,9,4,1] => [3,2,6,5,8,7,10,9,11,4,12,1] => 11011010100
[(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] => 10111010100
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [3,2,4,1,6,5,8,7,10,9,12,11] => 11001010101
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [4,3,6,5,8,7,9,2,11,10,12,1] => 11101010010
[(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] => 10101010110
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [4,3,6,5,8,7,9,2,10,1,12,11] => 11101010001
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [3,2,4,1,6,5,8,7,11,10,12,9] => 11001010110
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [5,4,8,7,9,6,10,3,11,2,12,1] => 11110110000
[(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] => 10110110001
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [3,2,5,4,8,7,9,6,11,10,12,1] => 11010110010
[(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] => 10110110010
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [3,2,5,4,8,7,9,6,10,1,12,11] => 11010110001
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [4,3,8,7,9,6,10,5,11,2,12,1] => 11101110000
[(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] => 10101110001
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [3,2,8,7,9,6,10,5,11,4,12,1] => 11011110000
[(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] => 10111110000
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [3,2,4,1,8,7,9,6,10,5,12,11] => 11001110001
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [4,3,5,2,8,7,9,6,11,10,12,1] => 11100110010
[(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] => 10101110010
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [4,3,5,2,8,7,9,6,10,1,12,11] => 11100110001
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [3,2,4,1,8,7,9,6,11,10,12,5] => 11001110010
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [5,4,6,3,8,7,10,9,11,2,12,1] => 11110010100
[(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] => 10110010101
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [3,2,5,4,8,7,10,9,11,6,12,1] => 11010110100
[(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] => 10110110100
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [3,2,5,4,6,1,8,7,10,9,12,11] => 11010010101
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [5,4,6,3,8,7,9,2,11,10,12,1] => 11110010010
[(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] => 10110010110
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [5,4,6,3,8,7,9,2,10,1,12,11] => 11110010001
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [3,2,5,4,6,1,8,7,11,10,12,9] => 11010010110
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [4,3,5,2,8,7,10,9,11,6,12,1] => 11100110100
[(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] => 10101110100
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [4,3,5,2,6,1,8,7,10,9,12,11] => 11100010101
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [3,2,4,1,8,7,10,9,11,6,12,5] => 11001110100
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [4,3,5,2,6,1,8,7,11,10,12,9] => 11100010110
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [6,5,7,4,9,8,10,3,11,2,12,1] => 11111001000
[(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] => 10111001001
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [3,2,6,5,7,4,9,8,11,10,12,1] => 11011001010
[(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] => 10111001010
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [3,2,6,5,7,4,9,8,10,1,12,11] => 11011001001
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [4,3,6,5,9,8,10,7,11,2,12,1] => 11101011000
[(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] => 10101011001
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [3,2,6,5,9,8,10,7,11,4,12,1] => 11011011000
[(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] => 10111011000
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [3,2,4,1,6,5,9,8,10,7,12,11] => 11001011001
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [4,3,6,5,7,2,9,8,11,10,12,1] => 11101001010
[(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] => 10101011010
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [4,3,6,5,7,2,9,8,10,1,12,11] => 11101001001
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [3,2,4,1,6,5,9,8,11,10,12,7] => 11001011010
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [6,5,7,4,8,3,10,9,11,2,12,1] => 11111000100
[(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] => 10111000101
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [3,2,6,5,7,4,10,9,11,8,12,1] => 11011001100
[(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] => 10111001100
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [3,2,6,5,7,4,8,1,10,9,12,11] => 11011000101
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [6,5,7,4,8,3,9,2,11,10,12,1] => 11111000010
[(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] => 10111000110
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [6,5,7,4,8,3,9,2,10,1,12,11] => 11111000001
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [3,2,6,5,7,4,8,1,11,10,12,9] => 11011000110
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [4,3,6,5,7,2,10,9,11,8,12,1] => 11101001100
[(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] => 10101011100
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [4,3,6,5,7,2,8,1,10,9,12,11] => 11101000101
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [3,2,4,1,6,5,10,9,11,8,12,7] => 11001011100
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [4,3,6,5,7,2,8,1,11,10,12,9] => 11101000110
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [5,4,6,3,9,8,10,7,11,2,12,1] => 11110011000
[(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] => 10110011001
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [3,2,5,4,9,8,10,7,11,6,12,1] => 11010111000
[(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] => 10110111000
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [3,2,5,4,6,1,9,8,10,7,12,11] => 11010011001
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [5,4,6,3,7,2,9,8,11,10,12,1] => 11110001010
[(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] => 10110011010
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [5,4,6,3,7,2,9,8,10,1,12,11] => 11110001001
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [3,2,5,4,6,1,9,8,11,10,12,7] => 11010011010
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [4,3,5,2,9,8,10,7,11,6,12,1] => 11100111000
[(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] => 10101111000
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [4,3,5,2,6,1,9,8,10,7,12,11] => 11100011001
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [3,2,4,1,9,8,10,7,11,6,12,5] => 11001111000
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [4,3,5,2,6,1,9,8,11,10,12,7] => 11100011010
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [5,4,6,3,7,2,10,9,11,8,12,1] => 11110001100
[(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] => 10110011100
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [5,4,6,3,7,2,8,1,10,9,12,11] => 11110000101
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [3,2,5,4,6,1,10,9,11,8,12,7] => 11010011100
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [5,4,6,3,7,2,8,1,11,10,12,9] => 11110000110
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [4,3,5,2,6,1,10,9,11,8,12,7] => 11100011100
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,12,9,11,10] => 10101010110
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,10,7,9,8,12,11] => 10101011001
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,8,5,7,6,10,9,12,11] => 10101100101
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,8,5,7,6,12,9,11,10] => 10101100110
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,6,3,5,4,8,7,10,9,12,11] => 10110010101
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,6,3,5,4,8,7,12,9,11,10] => 10110010110
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,3,5,4,10,7,9,8,12,11] => 10110011001
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [4,1,3,2,6,5,8,7,10,9,12,11] => 11001010101
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [4,1,3,2,6,5,8,7,12,9,11,10] => 11001010110
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [4,1,3,2,6,5,10,7,9,8,12,11] => 11001011001
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [4,1,3,2,8,5,7,6,10,9,12,11] => 11001100101
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,1,3,2,8,5,7,6,12,9,11,10] => 11001100110
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [3,5,1,7,2,9,4,11,6,12,8,10] => [12,1,3,2,5,4,7,6,9,8,11,10] => 11010101010
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
Clarke-Steingrimsson-Zeng inverse
Description
The inverse of the Clarke-Steingrimsson-Zeng map, sending excedances to descents.
This is the inverse of the map $\Phi$ in [1, sec.3].
Map
descent bottoms
Description
The descent bottoms of a permutation as a binary word.