Identifier
Mp00058: Perfect matchings —to permutation⟶ Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00109: Permutations —descent word⟶ 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] => [4,3,2,1] => 111
[(1,4),(2,3)] => [4,3,2,1] => [3,4,1,2] => 010
[(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] => [4,3,2,1,6,5] => 11101
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [3,4,1,2,6,5] => 01001
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [3,6,1,5,4,2] => 01011
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [3,5,1,6,2,4] => 01010
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [4,6,5,2,1,3] => 01110
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [5,6,4,2,3,1] => 01101
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,5,4,3,2,1] => 11111
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [6,3,2,5,4,1] => 11011
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,5,4,3] => 10111
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,5,6,3,4] => 10010
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [5,3,2,6,1,4] => 11010
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [6,4,5,3,1,2] => 10110
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [5,4,6,1,3,2] => 10101
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [4,5,6,1,2,3] => 00100
[(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] => [4,3,2,1,6,5,8,7] => 1110101
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [3,4,1,2,6,5,8,7] => 0100101
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [3,6,1,5,4,2,8,7] => 0101101
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [3,5,1,6,2,4,8,7] => 0101001
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [3,5,1,8,2,7,6,4] => 0101011
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [3,5,1,7,2,8,4,6] => 0101010
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [4,7,5,2,1,8,3,6] => 0111010
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [4,8,5,2,1,7,6,3] => 0111011
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [4,6,5,2,1,3,8,7] => 0111001
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [5,6,4,2,3,1,8,7] => 0110101
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,5,4,3,2,1,8,7] => 1111101
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [6,3,2,5,4,1,8,7] => 1101101
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,5,4,3,8,7] => 1011101
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,5,6,3,4,8,7] => 1001001
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [5,3,2,6,1,4,8,7] => 1101001
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [6,4,5,3,1,2,8,7] => 1011001
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [5,4,6,1,3,2,8,7] => 1010101
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [4,5,6,1,2,3,8,7] => 0010001
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [4,5,8,1,2,7,6,3] => 0010011
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [4,5,7,1,2,8,3,6] => 0010010
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [4,6,8,1,7,3,2,5] => 0010110
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [4,7,8,1,6,3,5,2] => 0010101
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [7,4,8,1,6,5,3,2] => 1010111
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [5,4,8,1,3,7,6,2] => 1010011
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [8,4,5,3,1,7,6,2] => 1011011
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [5,3,2,8,1,7,6,4] => 1101011
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,5,8,3,7,6,4] => 1001011
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,5,7,3,8,4,6] => 1001010
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [5,3,2,7,1,8,4,6] => 1101010
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [7,4,5,3,1,8,2,6] => 1011010
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [5,4,7,1,3,8,2,6] => 1010010
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [6,4,8,1,7,5,2,3] => 1010110
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [6,4,7,1,8,2,5,3] => 1010101
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [4,6,7,1,8,2,3,5] => 0010100
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [5,6,8,7,2,1,3,4] => 0011100
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [6,5,8,7,2,1,4,3] => 1011101
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [7,5,8,6,2,4,1,3] => 1011010
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [8,5,7,6,4,2,1,3] => 1011110
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [8,4,6,3,7,2,1,5] => 1010110
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [6,3,2,8,7,4,1,5] => 1101110
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,6,8,7,4,3,5] => 1001110
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,7,8,6,4,5,3] => 1001101
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [7,3,2,8,6,4,5,1] => 1101101
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [8,4,7,3,6,2,5,1] => 1010101
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [8,6,7,5,4,2,3,1] => 1011101
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [7,6,8,5,2,4,3,1] => 1011011
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [6,7,8,5,2,3,4,1] => 0011001
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [5,7,8,6,2,3,1,4] => 0011010
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [5,8,7,6,3,2,1,4] => 0111110
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [6,8,7,5,3,2,4,1] => 0111101
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [7,8,6,5,3,4,2,1] => 0111011
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,7,6,5,4,3,2,1] => 1111111
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [8,7,4,3,6,5,2,1] => 1110111
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [8,3,2,7,6,5,4,1] => 1101111
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,7,6,5,4,3] => 1011111
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,8,5,4,7,6,3] => 1011011
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [8,3,2,5,4,7,6,1] => 1101011
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [8,5,4,3,2,7,6,1] => 1111011
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [5,8,4,2,3,7,6,1] => 0110011
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [7,8,4,2,6,5,3,1] => 0110111
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [4,8,7,2,6,3,5,1] => 0110101
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [4,8,6,2,7,3,1,5] => 0110110
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [3,6,1,8,7,4,2,5] => 0101110
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [3,7,1,8,6,4,5,2] => 0101101
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [3,8,1,7,6,5,4,2] => 0101111
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [3,8,1,5,4,7,6,2] => 0101011
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [3,4,1,2,8,7,6,5] => 0100111
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,3,2,1,8,7,6,5] => 1110111
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,7,6,5] => 1010111
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,7,8,5,6] => 1010010
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [4,3,2,1,7,8,5,6] => 1110010
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [3,4,1,2,7,8,5,6] => 0100010
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [3,7,1,5,4,8,2,6] => 0101010
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [3,8,1,6,7,5,2,4] => 0100110
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [3,7,1,6,8,2,5,4] => 0100101
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [3,6,1,7,8,2,4,5] => 0100100
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [4,7,6,2,8,1,3,5] => 0110100
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [6,7,4,2,8,1,5,3] => 0110101
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [6,8,4,2,7,5,1,3] => 0110110
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [5,7,4,2,3,8,1,6] => 0110010
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [7,5,4,3,2,8,1,6] => 1111010
>>> Load all 473 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [7,3,2,5,4,8,1,6] => 1101010
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,7,5,4,8,3,6] => 1011010
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,8,6,7,5,3,4] => 1010110
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [8,3,2,6,7,5,1,4] => 1100110
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [8,6,4,3,7,5,1,2] => 1110110
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [8,7,5,6,4,3,1,2] => 1101110
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [7,8,5,6,3,4,1,2] => 0101010
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [6,8,5,7,3,1,4,2] => 0101101
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [5,8,6,7,3,1,2,4] => 0101100
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [5,7,6,8,1,3,2,4] => 0101010
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [6,7,5,8,1,3,4,2] => 0101001
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [7,6,5,8,1,4,3,2] => 1101011
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [8,6,5,7,4,1,3,2] => 1101101
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [7,6,4,3,8,1,5,2] => 1110101
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [7,3,2,6,8,1,5,4] => 1100101
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,7,6,8,3,5,4] => 1010101
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,6,7,8,3,4,5] => 1000100
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [6,3,2,7,8,1,4,5] => 1100100
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [7,4,6,3,8,1,2,5] => 1010100
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [8,5,6,7,4,1,2,3] => 1001100
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [7,5,6,8,1,4,2,3] => 1001010
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [6,5,7,8,1,2,4,3] => 1001001
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [5,6,7,8,1,2,3,4] => 0001000
[(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] => [4,3,2,1,6,5,8,7,10,9] => 111010101
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [3,4,1,2,6,5,8,7,10,9] => 010010101
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [3,5,1,6,2,4,8,7,10,9] => 010100101
[(1,8),(2,3),(4,5),(6,7),(9,10)] => [8,3,2,5,4,7,6,1,10,9] => [3,5,1,7,2,8,4,6,10,9] => 010101001
[(1,10),(2,3),(4,5),(6,7),(8,9)] => [10,3,2,5,4,7,6,9,8,1] => [3,5,1,7,2,9,4,10,6,8] => 010101010
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [6,5,4,3,2,1,8,7,10,9] => 111110101
[(1,3),(2,5),(4,6),(7,8),(9,10)] => [3,5,1,6,2,4,8,7,10,9] => [6,3,2,5,4,1,8,7,10,9] => 110110101
[(1,2),(3,5),(4,6),(7,8),(9,10)] => [2,1,5,6,3,4,8,7,10,9] => [2,1,6,5,4,3,8,7,10,9] => 101110101
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,5,6,3,4,8,7,10,9] => 100100101
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [4,5,6,1,2,3,8,7,10,9] => 001000101
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [4,5,7,1,2,8,3,6,10,9] => 001001001
[(1,10),(2,5),(3,4),(6,7),(8,9)] => [10,5,4,3,2,7,6,9,8,1] => [4,5,7,1,2,9,3,10,6,8] => 001001010
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,5,7,3,8,4,6,10,9] => 100101001
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [4,6,7,1,8,2,3,5,10,9] => 001010001
[(1,10),(2,7),(3,4),(5,6),(8,9)] => [10,7,4,3,6,5,2,9,8,1] => [4,6,7,1,9,2,3,10,5,8] => 001010010
[(1,2),(3,10),(4,5),(6,7),(8,9)] => [2,1,10,5,4,7,6,9,8,3] => [2,1,5,7,3,9,4,10,6,8] => 100101010
[(1,10),(2,9),(3,4),(5,6),(7,8)] => [10,9,4,3,6,5,8,7,2,1] => [4,6,8,1,9,2,10,3,5,7] => 001010100
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [8,7,6,5,4,3,2,1,10,9] => 111111101
[(1,4),(2,6),(3,7),(5,8),(9,10)] => [4,6,7,1,8,2,3,5,10,9] => [8,7,4,3,6,5,2,1,10,9] => 111011101
[(1,3),(2,6),(4,7),(5,8),(9,10)] => [3,6,1,7,8,2,4,5,10,9] => [8,3,2,7,6,5,4,1,10,9] => 110111101
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,8,7,6,5,4,3,10,9] => 101111101
[(1,2),(3,5),(4,7),(6,8),(9,10)] => [2,1,5,7,3,8,4,6,10,9] => [2,1,8,5,4,7,6,3,10,9] => 101101101
[(1,3),(2,5),(4,7),(6,8),(9,10)] => [3,5,1,7,2,8,4,6,10,9] => [8,3,2,5,4,7,6,1,10,9] => 110101101
[(1,4),(2,5),(3,7),(6,8),(9,10)] => [4,5,7,1,2,8,3,6,10,9] => [8,5,4,3,2,7,6,1,10,9] => 111101101
[(1,3),(2,4),(5,7),(6,8),(9,10)] => [3,4,1,2,7,8,5,6,10,9] => [4,3,2,1,8,7,6,5,10,9] => 111011101
[(1,2),(3,4),(5,7),(6,8),(9,10)] => [2,1,4,3,7,8,5,6,10,9] => [2,1,4,3,8,7,6,5,10,9] => 101011101
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,7,8,5,6,10,9] => 101001001
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [3,4,1,2,7,8,5,6,10,9] => 010001001
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [3,6,1,7,8,2,4,5,10,9] => 010010001
[(1,10),(2,3),(4,7),(5,6),(8,9)] => [10,3,2,7,6,5,4,9,8,1] => [3,6,1,7,9,2,4,10,5,8] => 010010010
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,6,7,8,3,4,5,10,9] => 100010001
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [5,6,7,8,1,2,3,4,10,9] => 000100001
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [5,6,7,9,1,2,3,10,4,8] => 000100010
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,6,7,9,3,4,10,5,8] => 100010010
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [5,6,8,9,1,2,10,3,4,7] => 000100100
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,7,9,5,10,6,8] => 101001010
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [3,4,1,2,7,9,5,10,6,8] => 010001010
[(1,10),(2,3),(4,9),(5,6),(7,8)] => [10,3,2,9,6,5,8,7,4,1] => [3,6,1,8,9,2,10,4,5,7] => 010010100
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,6,8,9,3,10,4,5,7] => 100010100
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [5,7,8,9,1,10,2,3,4,6] => 000101000
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,9,8,7,6,5,4,3] => 101111111
[(1,3),(2,7),(4,8),(5,9),(6,10)] => [3,7,1,8,9,10,2,4,5,6] => [10,3,2,9,8,7,6,5,4,1] => 110111111
[(1,4),(2,7),(3,8),(5,9),(6,10)] => [4,7,8,1,9,10,2,3,5,6] => [10,9,4,3,8,7,6,5,2,1] => 111011111
[(1,5),(2,7),(3,8),(4,9),(6,10)] => [5,7,8,9,1,10,2,3,4,6] => [10,9,8,5,4,7,6,3,2,1] => 111101111
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,9,8,7,6,5,4,3,2,1] => 111111111
[(1,5),(2,6),(3,8),(4,9),(7,10)] => [5,6,8,9,1,2,10,3,4,7] => [10,9,6,5,4,3,8,7,2,1] => 111110111
[(1,4),(2,6),(3,8),(5,9),(7,10)] => [4,6,8,1,9,2,10,3,5,7] => [10,9,4,3,6,5,8,7,2,1] => 111010111
[(1,3),(2,6),(4,8),(5,9),(7,10)] => [3,6,1,8,9,2,10,4,5,7] => [10,3,2,9,6,5,8,7,4,1] => 110110111
[(1,2),(3,6),(4,8),(5,9),(7,10)] => [2,1,6,8,9,3,10,4,5,7] => [2,1,10,9,6,5,8,7,4,3] => 101110111
[(1,2),(3,5),(4,8),(6,9),(7,10)] => [2,1,5,8,3,9,10,4,6,7] => [2,1,10,5,4,9,8,7,6,3] => 101101111
[(1,3),(2,5),(4,8),(6,9),(7,10)] => [3,5,1,8,2,9,10,4,6,7] => [10,3,2,5,4,9,8,7,6,1] => 110101111
[(1,4),(2,5),(3,8),(6,9),(7,10)] => [4,5,8,1,2,9,10,3,6,7] => [10,5,4,3,2,9,8,7,6,1] => 111101111
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [4,3,2,1,10,9,8,7,6,5] => 111011111
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,10,9,8,7,6,5] => 101011111
[(1,2),(3,4),(5,7),(6,9),(8,10)] => [2,1,4,3,7,9,5,10,6,8] => [2,1,4,3,10,7,6,9,8,5] => 101011011
[(1,3),(2,4),(5,7),(6,9),(8,10)] => [3,4,1,2,7,9,5,10,6,8] => [4,3,2,1,10,7,6,9,8,5] => 111011011
[(1,4),(2,5),(3,7),(6,9),(8,10)] => [4,5,7,1,2,9,3,10,6,8] => [10,5,4,3,2,7,6,9,8,1] => 111101011
[(1,3),(2,5),(4,7),(6,9),(8,10)] => [3,5,1,7,2,9,4,10,6,8] => [10,3,2,5,4,7,6,9,8,1] => 110101011
[(1,2),(3,5),(4,7),(6,9),(8,10)] => [2,1,5,7,3,9,4,10,6,8] => [2,1,10,5,4,7,6,9,8,3] => 101101011
[(1,2),(3,6),(4,7),(5,9),(8,10)] => [2,1,6,7,9,3,4,10,5,8] => [2,1,10,7,6,5,4,9,8,3] => 101111011
[(1,3),(2,6),(4,7),(5,9),(8,10)] => [3,6,1,7,9,2,4,10,5,8] => [10,3,2,7,6,5,4,9,8,1] => 110111011
[(1,4),(2,6),(3,7),(5,9),(8,10)] => [4,6,7,1,9,2,3,10,5,8] => [10,7,4,3,6,5,2,9,8,1] => 111011011
[(1,5),(2,6),(3,7),(4,9),(8,10)] => [5,6,7,9,1,2,3,10,4,8] => [10,7,6,5,4,3,2,9,8,1] => 111111011
[(1,2),(3,5),(4,6),(7,9),(8,10)] => [2,1,5,6,3,4,9,10,7,8] => [2,1,6,5,4,3,10,9,8,7] => 101110111
[(1,3),(2,5),(4,6),(7,9),(8,10)] => [3,5,1,6,2,4,9,10,7,8] => [6,3,2,5,4,1,10,9,8,7] => 110110111
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [6,5,4,3,2,1,10,9,8,7] => 111110111
[(1,3),(2,4),(5,6),(7,9),(8,10)] => [3,4,1,2,6,5,9,10,7,8] => [4,3,2,1,6,5,10,9,8,7] => 111010111
[(1,2),(3,4),(5,6),(7,9),(8,10)] => [2,1,4,3,6,5,9,10,7,8] => [2,1,4,3,6,5,10,9,8,7] => 101010111
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,9,10,7,8] => 101010010
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [3,4,1,2,6,5,9,10,7,8] => 010010010
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [3,5,1,6,2,4,9,10,7,8] => 010100010
[(1,10),(2,3),(4,5),(6,9),(7,8)] => [10,3,2,5,4,9,8,7,6,1] => [3,5,1,8,2,9,10,4,6,7] => 010100100
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,5,6,3,4,9,10,7,8] => 100100010
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [4,5,6,1,2,3,9,10,7,8] => 001000010
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [4,5,8,1,2,9,10,3,6,7] => 001000100
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,5,8,3,9,10,4,6,7] => 100100100
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [4,7,8,1,9,10,2,3,5,6] => 001001000
[(1,5),(2,6),(3,7),(4,10),(8,9)] => [5,6,7,10,1,2,3,9,8,4] => [9,7,6,5,4,3,2,10,1,8] => 111111010
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,8,9,10,5,6,7] => 101000100
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [3,4,1,2,8,9,10,5,6,7] => 010000100
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [3,7,1,8,9,10,2,4,5,6] => 010001000
[(1,4),(2,5),(3,10),(6,9),(7,8)] => [4,5,10,1,2,9,8,7,6,3] => [8,5,4,3,2,9,10,1,6,7] => 111100100
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,7,8,9,10,3,4,5,6] => 100001000
[(1,3),(2,10),(4,9),(5,8),(6,7)] => [3,10,1,9,8,7,6,5,4,2] => [7,3,2,8,9,10,1,4,5,6] => 110001000
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [6,7,8,9,10,1,2,3,4,5] => 000010000
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [7,8,9,10,11,12,1,2,3,4,5,6] => 00000100000
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,7,8,9,10,3,4,5,6,12,11] => 10000100001
[(1,12),(2,3),(4,9),(5,8),(6,7),(10,11)] => [12,3,2,9,8,7,6,5,4,11,10,1] => [3,7,1,8,9,11,2,4,5,12,6,10] => 01000100010
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,7,8,9,11,3,4,5,12,6,10] => 10000100010
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [3,7,1,8,9,10,2,4,5,6,12,11] => 01000100001
[(1,12),(2,11),(3,4),(5,8),(6,7),(9,10)] => [12,11,4,3,8,7,6,5,10,9,2,1] => [4,7,8,1,10,11,2,3,12,5,6,9] => 00100100100
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,7,8,5,6,10,9,12,11] => 10100100101
[(1,12),(2,3),(4,11),(5,8),(6,7),(9,10)] => [12,3,2,11,8,7,6,5,10,9,4,1] => [3,7,1,8,10,11,2,4,12,5,6,9] => 01000100100
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,7,8,10,11,3,4,12,5,6,9] => 10000100100
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [3,4,1,2,7,8,5,6,10,9,12,11] => 01000100101
[(1,12),(2,9),(3,4),(5,8),(6,7),(10,11)] => [12,9,4,3,8,7,6,5,2,11,10,1] => [4,7,8,1,9,11,2,3,5,12,6,10] => 00100100010
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,7,8,5,6,11,12,9,10] => 10100100010
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [4,7,8,1,9,10,2,3,5,6,12,11] => 00100100001
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [3,4,1,2,7,8,5,6,11,12,9,10] => 01000100010
[(1,12),(2,11),(3,10),(4,5),(6,7),(8,9)] => [12,11,10,5,4,7,6,9,8,3,2,1] => [5,7,9,10,1,11,2,12,3,4,6,8] => 00010101000
[(1,2),(3,10),(4,5),(6,7),(8,9),(11,12)] => [2,1,10,5,4,7,6,9,8,3,12,11] => [2,1,5,7,3,9,4,10,6,8,12,11] => 10010101001
[(1,12),(2,3),(4,5),(6,7),(8,9),(10,11)] => [12,3,2,5,4,7,6,9,8,11,10,1] => [3,5,1,7,2,9,4,11,6,12,8,10] => 01010101010
[(1,2),(3,12),(4,5),(6,7),(8,9),(10,11)] => [2,1,12,5,4,7,6,9,8,11,10,3] => [2,1,5,7,3,9,4,11,6,12,8,10] => 10010101010
[(1,10),(2,3),(4,5),(6,7),(8,9),(11,12)] => [10,3,2,5,4,7,6,9,8,1,12,11] => [3,5,1,7,2,9,4,10,6,8,12,11] => 01010101001
[(1,12),(2,11),(3,4),(5,10),(6,7),(8,9)] => [12,11,4,3,10,7,6,9,8,5,2,1] => [4,7,9,1,10,11,2,12,3,5,6,8] => 00100101000
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,7,9,5,10,6,8,12,11] => 10100101001
[(1,12),(2,3),(4,11),(5,10),(6,7),(8,9)] => [12,3,2,11,10,7,6,9,8,5,4,1] => [3,7,1,9,10,11,2,12,4,5,6,8] => 01000101000
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,7,9,10,11,3,12,4,5,6,8] => 10000101000
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [3,4,1,2,7,9,5,10,6,8,12,11] => 01000101001
[(1,12),(2,5),(3,4),(6,7),(8,9),(10,11)] => [12,5,4,3,2,7,6,9,8,11,10,1] => [4,5,7,1,2,9,3,11,6,12,8,10] => 00100101010
[(1,2),(3,4),(5,12),(6,7),(8,9),(10,11)] => [2,1,4,3,12,7,6,9,8,11,10,5] => [2,1,4,3,7,9,5,11,6,12,8,10] => 10100101010
[(1,10),(2,5),(3,4),(6,7),(8,9),(11,12)] => [10,5,4,3,2,7,6,9,8,1,12,11] => [4,5,7,1,2,9,3,10,6,8,12,11] => 00100101001
[(1,4),(2,3),(5,12),(6,7),(8,9),(10,11)] => [4,3,2,1,12,7,6,9,8,11,10,5] => [3,4,1,2,7,9,5,11,6,12,8,10] => 01000101010
[(1,12),(2,11),(3,8),(4,5),(6,7),(9,10)] => [12,11,8,5,4,7,6,3,10,9,2,1] => [5,7,8,10,1,11,2,3,12,4,6,9] => 00010100100
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,5,7,3,8,4,6,10,9,12,11] => 10010100101
[(1,12),(2,3),(4,5),(6,7),(8,11),(9,10)] => [12,3,2,5,4,7,6,11,10,9,8,1] => [3,5,1,7,2,10,4,11,12,6,8,9] => 01010100100
[(1,2),(3,12),(4,5),(6,7),(8,11),(9,10)] => [2,1,12,5,4,7,6,11,10,9,8,3] => [2,1,5,7,3,10,4,11,12,6,8,9] => 10010100100
[(1,8),(2,3),(4,5),(6,7),(9,10),(11,12)] => [8,3,2,5,4,7,6,1,10,9,12,11] => [3,5,1,7,2,8,4,6,10,9,12,11] => 01010100101
[(1,12),(2,9),(3,8),(4,5),(6,7),(10,11)] => [12,9,8,5,4,7,6,3,2,11,10,1] => [5,7,8,9,1,11,2,3,4,12,6,10] => 00010100010
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,5,7,3,8,4,6,11,12,9,10] => 10010100010
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [5,7,8,9,1,10,2,3,4,6,12,11] => 00010100001
[(1,8),(2,3),(4,5),(6,7),(9,12),(10,11)] => [8,3,2,5,4,7,6,1,12,11,10,9] => [3,5,1,7,2,8,4,6,11,12,9,10] => 01010100010
[(1,12),(2,5),(3,4),(6,7),(8,11),(9,10)] => [12,5,4,3,2,7,6,11,10,9,8,1] => [4,5,7,1,2,10,3,11,12,6,8,9] => 00100100100
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,7,10,5,11,12,6,8,9] => 10100100100
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [4,5,7,1,2,8,3,6,10,9,12,11] => 00100100101
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [3,4,1,2,7,10,5,11,12,6,8,9] => 01000100100
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [4,5,7,1,2,8,3,6,11,12,9,10] => 00100100010
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [6,8,9,10,11,1,12,2,3,4,5,7] => 00001010000
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,6,8,9,3,10,4,5,7,12,11] => 10001010001
[(1,12),(2,3),(4,9),(5,6),(7,8),(10,11)] => [12,3,2,9,6,5,8,7,4,11,10,1] => [3,6,1,8,9,2,11,4,5,12,7,10] => 01001010010
[(1,2),(3,12),(4,9),(5,6),(7,8),(10,11)] => [2,1,12,9,6,5,8,7,4,11,10,3] => [2,1,6,8,9,3,11,4,5,12,7,10] => 10001010010
[(1,10),(2,3),(4,9),(5,6),(7,8),(11,12)] => [10,3,2,9,6,5,8,7,4,1,12,11] => [3,6,1,8,9,2,10,4,5,7,12,11] => 01001010001
[(1,12),(2,11),(3,4),(5,6),(7,8),(9,10)] => [12,11,4,3,6,5,8,7,10,9,2,1] => [4,6,8,1,10,2,11,3,12,5,7,9] => 00101010100
[(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] => [3,6,1,8,10,2,11,4,12,5,7,9] => 01001010100
[(1,2),(3,12),(4,11),(5,6),(7,8),(9,10)] => [2,1,12,11,6,5,8,7,10,9,4,3] => [2,1,6,8,10,3,11,4,12,5,7,9] => 10001010100
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [3,4,1,2,6,5,8,7,10,9,12,11] => 01001010101
[(1,12),(2,9),(3,4),(5,6),(7,8),(10,11)] => [12,9,4,3,6,5,8,7,2,11,10,1] => [4,6,8,1,9,2,11,3,5,12,7,10] => 00101010010
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,11,12,9,10] => 10101010010
[(1,10),(2,9),(3,4),(5,6),(7,8),(11,12)] => [10,9,4,3,6,5,8,7,2,1,12,11] => [4,6,8,1,9,2,10,3,5,7,12,11] => 00101010001
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [3,4,1,2,6,5,8,7,11,12,9,10] => 01001010010
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [5,8,9,10,1,11,12,2,3,4,6,7] => 00010010000
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,5,8,3,9,10,4,6,7,12,11] => 10010010001
[(1,12),(2,3),(4,5),(6,9),(7,8),(10,11)] => [12,3,2,5,4,9,8,7,6,11,10,1] => [3,5,1,8,2,9,11,4,6,12,7,10] => 01010010010
[(1,2),(3,12),(4,5),(6,9),(7,8),(10,11)] => [2,1,12,5,4,9,8,7,6,11,10,3] => [2,1,5,8,3,9,11,4,6,12,7,10] => 10010010010
[(1,10),(2,3),(4,5),(6,9),(7,8),(11,12)] => [10,3,2,5,4,9,8,7,6,1,12,11] => [3,5,1,8,2,9,10,4,6,7,12,11] => 01010010001
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [4,8,9,1,10,11,12,2,3,5,6,7] => 00100010000
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,8,9,10,5,6,7,12,11] => 10100010001
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [3,8,1,9,10,11,12,2,4,5,6,7] => 01000010000
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,8,9,10,11,12,3,4,5,6,7] => 10000010000
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [3,4,1,2,8,9,10,5,6,7,12,11] => 01000010001
[(1,12),(2,5),(3,4),(6,9),(7,8),(10,11)] => [12,5,4,3,2,9,8,7,6,11,10,1] => [4,5,8,1,2,9,11,3,6,12,7,10] => 00100010010
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,8,9,11,5,6,12,7,10] => 10100010010
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [4,5,8,1,2,9,10,3,6,7,12,11] => 00100010001
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [3,4,1,2,8,9,11,5,6,12,7,10] => 01000010010
[(1,12),(2,11),(3,6),(4,5),(7,8),(9,10)] => [12,11,6,5,4,3,8,7,10,9,2,1] => [5,6,8,10,1,2,11,3,12,4,7,9] => 00010010100
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,5,6,3,4,8,7,10,9,12,11] => 10010010101
[(1,12),(2,3),(4,5),(6,11),(7,8),(9,10)] => [12,3,2,5,4,11,8,7,10,9,6,1] => [3,5,1,8,2,10,11,4,12,6,7,9] => 01010010100
[(1,2),(3,12),(4,5),(6,11),(7,8),(9,10)] => [2,1,12,5,4,11,8,7,10,9,6,3] => [2,1,5,8,3,10,11,4,12,6,7,9] => 10010010100
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [3,5,1,6,2,4,8,7,10,9,12,11] => 01010010101
[(1,12),(2,9),(3,6),(4,5),(7,8),(10,11)] => [12,9,6,5,4,3,8,7,2,11,10,1] => [5,6,8,9,1,2,11,3,4,12,7,10] => 00010010010
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,5,6,3,4,8,7,11,12,9,10] => 10010010010
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [5,6,8,9,1,2,10,3,4,7,12,11] => 00010010001
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [3,5,1,6,2,4,8,7,11,12,9,10] => 01010010010
[(1,12),(2,5),(3,4),(6,11),(7,8),(9,10)] => [12,5,4,3,2,11,8,7,10,9,6,1] => [4,5,8,1,2,10,11,3,12,6,7,9] => 00100010100
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,8,10,11,5,12,6,7,9] => 10100010100
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [4,5,6,1,2,3,8,7,10,9,12,11] => 00100010101
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [3,4,1,2,8,10,11,5,12,6,7,9] => 01000010100
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [4,5,6,1,2,3,8,7,11,12,9,10] => 00100010010
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [6,7,9,10,11,1,2,12,3,4,5,8] => 00001001000
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,6,7,9,3,4,10,5,8,12,11] => 10001001001
[(1,12),(2,3),(4,7),(5,6),(8,9),(10,11)] => [12,3,2,7,6,5,4,9,8,11,10,1] => [3,6,1,7,9,2,4,11,5,12,8,10] => 01001001010
[(1,2),(3,12),(4,7),(5,6),(8,9),(10,11)] => [2,1,12,7,6,5,4,9,8,11,10,3] => [2,1,6,7,9,3,4,11,5,12,8,10] => 10001001010
[(1,10),(2,3),(4,7),(5,6),(8,9),(11,12)] => [10,3,2,7,6,5,4,9,8,1,12,11] => [3,6,1,7,9,2,4,10,5,8,12,11] => 01001001001
[(1,12),(2,11),(3,4),(5,6),(7,10),(8,9)] => [12,11,4,3,6,5,10,9,8,7,2,1] => [4,6,9,1,10,2,11,12,3,5,7,8] => 00101001000
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,9,10,7,8,12,11] => 10101001001
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [3,6,1,9,10,2,11,12,4,5,7,8] => 01001001000
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,6,9,10,3,11,12,4,5,7,8] => 10001001000
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [3,4,1,2,6,5,9,10,7,8,12,11] => 01001001001
[(1,12),(2,7),(3,4),(5,6),(8,9),(10,11)] => [12,7,4,3,6,5,2,9,8,11,10,1] => [4,6,7,1,9,2,3,11,5,12,8,10] => 00101001010
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,9,11,7,12,8,10] => 10101001010
[(1,10),(2,7),(3,4),(5,6),(8,9),(11,12)] => [10,7,4,3,6,5,2,9,8,1,12,11] => [4,6,7,1,9,2,3,10,5,8,12,11] => 00101001001
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [3,4,1,2,6,5,9,11,7,12,8,10] => 01001001010
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [6,7,8,10,11,1,2,3,12,4,5,9] => 00001000100
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,6,7,8,3,4,5,10,9,12,11] => 10001000101
[(1,12),(2,3),(4,7),(5,6),(8,11),(9,10)] => [12,3,2,7,6,5,4,11,10,9,8,1] => [3,6,1,7,10,2,4,11,12,5,8,9] => 01001000100
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,6,7,10,3,4,11,12,5,8,9] => 10001000100
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [3,6,1,7,8,2,4,5,10,9,12,11] => 01001000101
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [6,7,8,9,11,1,2,3,4,12,5,10] => 00001000010
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,6,7,8,3,4,5,11,12,9,10] => 10001000010
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [6,7,8,9,10,1,2,3,4,5,12,11] => 00001000001
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [3,6,1,7,8,2,4,5,11,12,9,10] => 01001000010
[(1,12),(2,7),(3,4),(5,6),(8,11),(9,10)] => [12,7,4,3,6,5,2,11,10,9,8,1] => [4,6,7,1,10,2,3,11,12,5,8,9] => 00101000100
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,10,11,12,7,8,9] => 10101000100
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [4,6,7,1,8,2,3,5,10,9,12,11] => 00101000101
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [3,4,1,2,6,5,10,11,12,7,8,9] => 01001000100
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [4,6,7,1,8,2,3,5,11,12,9,10] => 00101000010
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [5,6,9,10,1,2,11,12,3,4,7,8] => 00010001000
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,5,6,3,4,9,10,7,8,12,11] => 10010001001
[(1,12),(2,3),(4,5),(6,11),(7,10),(8,9)] => [12,3,2,5,4,11,10,9,8,7,6,1] => [3,5,1,9,2,10,11,12,4,6,7,8] => 01010001000
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,5,9,3,10,11,12,4,6,7,8] => 10010001000
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [3,5,1,6,2,4,9,10,7,8,12,11] => 01010001001
[(1,12),(2,7),(3,6),(4,5),(8,9),(10,11)] => [12,7,6,5,4,3,2,9,8,11,10,1] => [5,6,7,9,1,2,3,11,4,12,8,10] => 00010001010
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,5,6,3,4,9,11,7,12,8,10] => 10010001010
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [5,6,7,9,1,2,3,10,4,8,12,11] => 00010001001
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [3,5,1,6,2,4,9,11,7,12,8,10] => 01010001010
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [4,5,9,1,2,10,11,12,3,6,7,8] => 00100001000
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,9,10,11,12,5,6,7,8] => 10100001000
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [4,5,6,1,2,3,9,10,7,8,12,11] => 00100001001
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [3,4,1,2,9,10,11,12,5,6,7,8] => 01000001000
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [4,5,6,1,2,3,9,11,7,12,8,10] => 00100001010
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [5,6,7,10,1,2,3,11,12,4,8,9] => 00010000100
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,5,6,3,4,10,11,12,7,8,9] => 10010000100
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [5,6,7,8,1,2,3,4,10,9,12,11] => 00010000101
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [3,5,1,6,2,4,10,11,12,7,8,9] => 01010000100
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [5,6,7,8,1,2,3,4,11,12,9,10] => 00010000010
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [4,5,6,1,2,3,10,11,12,7,8,9] => 00100000100
[(1,2),(3,4),(5,6),(7,8),(9,11),(10,12)] => [2,1,4,3,6,5,8,7,11,12,9,10] => [2,1,4,3,6,5,8,7,12,11,10,9] => 10101010111
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)] => [2,1,4,3,6,5,9,10,7,8,12,11] => [2,1,4,3,6,5,10,9,8,7,12,11] => 10101011101
[(1,2),(3,4),(5,6),(7,9),(8,11),(10,12)] => [2,1,4,3,6,5,9,11,7,12,8,10] => [2,1,4,3,6,5,12,9,8,11,10,7] => 10101011011
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,12,11,10,9,8,7] => 10101011111
[(1,2),(3,4),(5,7),(6,8),(9,10),(11,12)] => [2,1,4,3,7,8,5,6,10,9,12,11] => [2,1,4,3,8,7,6,5,10,9,12,11] => 10101110101
[(1,2),(3,4),(5,7),(6,8),(9,11),(10,12)] => [2,1,4,3,7,8,5,6,11,12,9,10] => [2,1,4,3,8,7,6,5,12,11,10,9] => 10101110111
[(1,2),(3,4),(5,7),(6,9),(8,10),(11,12)] => [2,1,4,3,7,9,5,10,6,8,12,11] => [2,1,4,3,10,7,6,9,8,5,12,11] => 10101101101
[(1,2),(3,4),(5,7),(6,9),(8,11),(10,12)] => [2,1,4,3,7,9,5,11,6,12,8,10] => [2,1,4,3,12,7,6,9,8,11,10,5] => 10101101011
[(1,2),(3,4),(5,7),(6,10),(8,11),(9,12)] => [2,1,4,3,7,10,5,11,12,6,8,9] => [2,1,4,3,12,7,6,11,10,9,8,5] => 10101101111
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,10,9,8,7,6,5,12,11] => 10101111101
[(1,2),(3,4),(5,8),(6,9),(7,11),(10,12)] => [2,1,4,3,8,9,11,5,6,12,7,10] => [2,1,4,3,12,9,8,7,6,11,10,5] => 10101111011
[(1,2),(3,4),(5,8),(6,10),(7,11),(9,12)] => [2,1,4,3,8,10,11,5,12,6,7,9] => [2,1,4,3,12,11,8,7,10,9,6,5] => 10101110111
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,12,11,10,9,8,7,6,5] => 10101111111
[(1,2),(3,5),(4,6),(7,8),(9,10),(11,12)] => [2,1,5,6,3,4,8,7,10,9,12,11] => [2,1,6,5,4,3,8,7,10,9,12,11] => 10111010101
[(1,2),(3,5),(4,6),(7,8),(9,11),(10,12)] => [2,1,5,6,3,4,8,7,11,12,9,10] => [2,1,6,5,4,3,8,7,12,11,10,9] => 10111010111
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)] => [2,1,5,6,3,4,9,10,7,8,12,11] => [2,1,6,5,4,3,10,9,8,7,12,11] => 10111011101
[(1,2),(3,5),(4,6),(7,9),(8,11),(10,12)] => [2,1,5,6,3,4,9,11,7,12,8,10] => [2,1,6,5,4,3,12,9,8,11,10,7] => 10111011011
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,6,5,4,3,12,11,10,9,8,7] => 10111011111
[(1,2),(3,5),(4,7),(6,8),(9,10),(11,12)] => [2,1,5,7,3,8,4,6,10,9,12,11] => [2,1,8,5,4,7,6,3,10,9,12,11] => 10110110101
[(1,2),(3,5),(4,7),(6,8),(9,11),(10,12)] => [2,1,5,7,3,8,4,6,11,12,9,10] => [2,1,8,5,4,7,6,3,12,11,10,9] => 10110110111
[(1,2),(3,5),(4,7),(6,9),(8,10),(11,12)] => [2,1,5,7,3,9,4,10,6,8,12,11] => [2,1,10,5,4,7,6,9,8,3,12,11] => 10110101101
[(1,2),(3,5),(4,7),(6,9),(8,11),(10,12)] => [2,1,5,7,3,9,4,11,6,12,8,10] => [2,1,12,5,4,7,6,9,8,11,10,3] => 10110101011
[(1,2),(3,5),(4,7),(6,10),(8,11),(9,12)] => [2,1,5,7,3,10,4,11,12,6,8,9] => [2,1,12,5,4,7,6,11,10,9,8,3] => 10110101111
[(1,2),(3,5),(4,8),(6,9),(7,10),(11,12)] => [2,1,5,8,3,9,10,4,6,7,12,11] => [2,1,10,5,4,9,8,7,6,3,12,11] => 10110111101
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,12)] => [2,1,5,8,3,9,11,4,6,12,7,10] => [2,1,12,5,4,9,8,7,6,11,10,3] => 10110111011
[(1,2),(3,5),(4,8),(6,10),(7,11),(9,12)] => [2,1,5,8,3,10,11,4,12,6,7,9] => [2,1,12,5,4,11,8,7,10,9,6,3] => 10110110111
[(1,2),(3,5),(4,9),(6,10),(7,11),(8,12)] => [2,1,5,9,3,10,11,12,4,6,7,8] => [2,1,12,5,4,11,10,9,8,7,6,3] => 10110111111
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,8,7,6,5,4,3,10,9,12,11] => 10111110101
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,8,7,6,5,4,3,12,11,10,9] => 10111110111
[(1,2),(3,6),(4,7),(5,9),(8,10),(11,12)] => [2,1,6,7,9,3,4,10,5,8,12,11] => [2,1,10,7,6,5,4,9,8,3,12,11] => 10111101101
[(1,2),(3,6),(4,7),(5,9),(8,11),(10,12)] => [2,1,6,7,9,3,4,11,5,12,8,10] => [2,1,12,7,6,5,4,9,8,11,10,3] => 10111101011
[(1,2),(3,6),(4,7),(5,10),(8,11),(9,12)] => [2,1,6,7,10,3,4,11,12,5,8,9] => [2,1,12,7,6,5,4,11,10,9,8,3] => 10111101111
[(1,2),(3,6),(4,8),(5,9),(7,10),(11,12)] => [2,1,6,8,9,3,10,4,5,7,12,11] => [2,1,10,9,6,5,8,7,4,3,12,11] => 10111011101
[(1,2),(3,6),(4,8),(5,9),(7,11),(10,12)] => [2,1,6,8,9,3,11,4,5,12,7,10] => [2,1,12,9,6,5,8,7,4,11,10,3] => 10111011011
[(1,2),(3,6),(4,8),(5,10),(7,11),(9,12)] => [2,1,6,8,10,3,11,4,12,5,7,9] => [2,1,12,11,6,5,8,7,10,9,4,3] => 10111010111
[(1,2),(3,6),(4,9),(5,10),(7,11),(8,12)] => [2,1,6,9,10,3,11,12,4,5,7,8] => [2,1,12,11,6,5,10,9,8,7,4,3] => 10111011111
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,10,9,8,7,6,5,4,3,12,11] => 10111111101
[(1,2),(3,7),(4,8),(5,9),(6,11),(10,12)] => [2,1,7,8,9,11,3,4,5,12,6,10] => [2,1,12,9,8,7,6,5,4,11,10,3] => 10111111011
[(1,2),(3,7),(4,8),(5,10),(6,11),(9,12)] => [2,1,7,8,10,11,3,4,12,5,6,9] => [2,1,12,11,8,7,6,5,10,9,4,3] => 10111110111
[(1,2),(3,7),(4,9),(5,10),(6,11),(8,12)] => [2,1,7,9,10,11,3,12,4,5,6,8] => [2,1,12,11,10,7,6,9,8,5,4,3] => 10111101111
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,12,11,10,9,8,7,6,5,4,3] => 10111111111
[(1,3),(2,4),(5,6),(7,8),(9,10),(11,12)] => [3,4,1,2,6,5,8,7,10,9,12,11] => [4,3,2,1,6,5,8,7,10,9,12,11] => 11101010101
[(1,3),(2,4),(5,6),(7,8),(9,11),(10,12)] => [3,4,1,2,6,5,8,7,11,12,9,10] => [4,3,2,1,6,5,8,7,12,11,10,9] => 11101010111
[(1,3),(2,4),(5,6),(7,9),(8,10),(11,12)] => [3,4,1,2,6,5,9,10,7,8,12,11] => [4,3,2,1,6,5,10,9,8,7,12,11] => 11101011101
[(1,3),(2,4),(5,6),(7,9),(8,11),(10,12)] => [3,4,1,2,6,5,9,11,7,12,8,10] => [4,3,2,1,6,5,12,9,8,11,10,7] => 11101011011
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [4,3,2,1,6,5,12,11,10,9,8,7] => 11101011111
[(1,3),(2,4),(5,7),(6,8),(9,10),(11,12)] => [3,4,1,2,7,8,5,6,10,9,12,11] => [4,3,2,1,8,7,6,5,10,9,12,11] => 11101110101
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12)] => [3,4,1,2,7,8,5,6,11,12,9,10] => [4,3,2,1,8,7,6,5,12,11,10,9] => 11101110111
[(1,3),(2,4),(5,7),(6,9),(8,10),(11,12)] => [3,4,1,2,7,9,5,10,6,8,12,11] => [4,3,2,1,10,7,6,9,8,5,12,11] => 11101101101
[(1,3),(2,4),(5,7),(6,9),(8,11),(10,12)] => [3,4,1,2,7,9,5,11,6,12,8,10] => [4,3,2,1,12,7,6,9,8,11,10,5] => 11101101011
[(1,3),(2,4),(5,7),(6,10),(8,11),(9,12)] => [3,4,1,2,7,10,5,11,12,6,8,9] => [4,3,2,1,12,7,6,11,10,9,8,5] => 11101101111
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [4,3,2,1,10,9,8,7,6,5,12,11] => 11101111101
[(1,3),(2,4),(5,8),(6,9),(7,11),(10,12)] => [3,4,1,2,8,9,11,5,6,12,7,10] => [4,3,2,1,12,9,8,7,6,11,10,5] => 11101111011
[(1,3),(2,4),(5,8),(6,10),(7,11),(9,12)] => [3,4,1,2,8,10,11,5,12,6,7,9] => [4,3,2,1,12,11,8,7,10,9,6,5] => 11101110111
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [4,3,2,1,12,11,10,9,8,7,6,5] => 11101111111
[(1,3),(2,5),(4,6),(7,8),(9,10),(11,12)] => [3,5,1,6,2,4,8,7,10,9,12,11] => [6,3,2,5,4,1,8,7,10,9,12,11] => 11011010101
[(1,3),(2,5),(4,6),(7,8),(9,11),(10,12)] => [3,5,1,6,2,4,8,7,11,12,9,10] => [6,3,2,5,4,1,8,7,12,11,10,9] => 11011010111
[(1,3),(2,5),(4,6),(7,9),(8,10),(11,12)] => [3,5,1,6,2,4,9,10,7,8,12,11] => [6,3,2,5,4,1,10,9,8,7,12,11] => 11011011101
[(1,3),(2,5),(4,6),(7,9),(8,11),(10,12)] => [3,5,1,6,2,4,9,11,7,12,8,10] => [6,3,2,5,4,1,12,9,8,11,10,7] => 11011011011
[(1,3),(2,5),(4,6),(7,10),(8,11),(9,12)] => [3,5,1,6,2,4,10,11,12,7,8,9] => [6,3,2,5,4,1,12,11,10,9,8,7] => 11011011111
[(1,3),(2,5),(4,7),(6,8),(9,10),(11,12)] => [3,5,1,7,2,8,4,6,10,9,12,11] => [8,3,2,5,4,7,6,1,10,9,12,11] => 11010110101
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,12)] => [3,5,1,7,2,8,4,6,11,12,9,10] => [8,3,2,5,4,7,6,1,12,11,10,9] => 11010110111
[(1,3),(2,5),(4,7),(6,9),(8,10),(11,12)] => [3,5,1,7,2,9,4,10,6,8,12,11] => [10,3,2,5,4,7,6,9,8,1,12,11] => 11010101101
[(1,3),(2,5),(4,7),(6,9),(8,11),(10,12)] => [3,5,1,7,2,9,4,11,6,12,8,10] => [12,3,2,5,4,7,6,9,8,11,10,1] => 11010101011
[(1,3),(2,5),(4,7),(6,10),(8,11),(9,12)] => [3,5,1,7,2,10,4,11,12,6,8,9] => [12,3,2,5,4,7,6,11,10,9,8,1] => 11010101111
[(1,3),(2,5),(4,8),(6,9),(7,10),(11,12)] => [3,5,1,8,2,9,10,4,6,7,12,11] => [10,3,2,5,4,9,8,7,6,1,12,11] => 11010111101
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,12)] => [3,5,1,8,2,9,11,4,6,12,7,10] => [12,3,2,5,4,9,8,7,6,11,10,1] => 11010111011
[(1,3),(2,5),(4,8),(6,10),(7,11),(9,12)] => [3,5,1,8,2,10,11,4,12,6,7,9] => [12,3,2,5,4,11,8,7,10,9,6,1] => 11010110111
[(1,3),(2,5),(4,9),(6,10),(7,11),(8,12)] => [3,5,1,9,2,10,11,12,4,6,7,8] => [12,3,2,5,4,11,10,9,8,7,6,1] => 11010111111
[(1,3),(2,6),(4,7),(5,8),(9,10),(11,12)] => [3,6,1,7,8,2,4,5,10,9,12,11] => [8,3,2,7,6,5,4,1,10,9,12,11] => 11011110101
[(1,3),(2,6),(4,7),(5,8),(9,11),(10,12)] => [3,6,1,7,8,2,4,5,11,12,9,10] => [8,3,2,7,6,5,4,1,12,11,10,9] => 11011110111
[(1,3),(2,6),(4,7),(5,9),(8,10),(11,12)] => [3,6,1,7,9,2,4,10,5,8,12,11] => [10,3,2,7,6,5,4,9,8,1,12,11] => 11011101101
[(1,3),(2,6),(4,7),(5,9),(8,11),(10,12)] => [3,6,1,7,9,2,4,11,5,12,8,10] => [12,3,2,7,6,5,4,9,8,11,10,1] => 11011101011
[(1,3),(2,6),(4,7),(5,10),(8,11),(9,12)] => [3,6,1,7,10,2,4,11,12,5,8,9] => [12,3,2,7,6,5,4,11,10,9,8,1] => 11011101111
[(1,3),(2,6),(4,8),(5,9),(7,10),(11,12)] => [3,6,1,8,9,2,10,4,5,7,12,11] => [10,3,2,9,6,5,8,7,4,1,12,11] => 11011011101
[(1,3),(2,6),(4,8),(5,9),(7,11),(10,12)] => [3,6,1,8,9,2,11,4,5,12,7,10] => [12,3,2,9,6,5,8,7,4,11,10,1] => 11011011011
[(1,3),(2,6),(4,8),(5,10),(7,11),(9,12)] => [3,6,1,8,10,2,11,4,12,5,7,9] => [12,3,2,11,6,5,8,7,10,9,4,1] => 11011010111
[(1,3),(2,6),(4,9),(5,10),(7,11),(8,12)] => [3,6,1,9,10,2,11,12,4,5,7,8] => [12,3,2,11,6,5,10,9,8,7,4,1] => 11011011111
[(1,3),(2,7),(4,8),(5,9),(6,10),(11,12)] => [3,7,1,8,9,10,2,4,5,6,12,11] => [10,3,2,9,8,7,6,5,4,1,12,11] => 11011111101
[(1,3),(2,7),(4,8),(5,9),(6,11),(10,12)] => [3,7,1,8,9,11,2,4,5,12,6,10] => [12,3,2,9,8,7,6,5,4,11,10,1] => 11011111011
[(1,3),(2,7),(4,8),(5,10),(6,11),(9,12)] => [3,7,1,8,10,11,2,4,12,5,6,9] => [12,3,2,11,8,7,6,5,10,9,4,1] => 11011110111
[(1,3),(2,7),(4,9),(5,10),(6,11),(8,12)] => [3,7,1,9,10,11,2,12,4,5,6,8] => [12,3,2,11,10,7,6,9,8,5,4,1] => 11011101111
[(1,3),(2,8),(4,9),(5,10),(6,11),(7,12)] => [3,8,1,9,10,11,12,2,4,5,6,7] => [12,3,2,11,10,9,8,7,6,5,4,1] => 11011111111
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [6,5,4,3,2,1,8,7,10,9,12,11] => 11111010101
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [6,5,4,3,2,1,8,7,12,11,10,9] => 11111010111
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [6,5,4,3,2,1,10,9,8,7,12,11] => 11111011101
[(1,4),(2,5),(3,6),(7,9),(8,11),(10,12)] => [4,5,6,1,2,3,9,11,7,12,8,10] => [6,5,4,3,2,1,12,9,8,11,10,7] => 11111011011
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [6,5,4,3,2,1,12,11,10,9,8,7] => 11111011111
[(1,4),(2,5),(3,7),(6,8),(9,10),(11,12)] => [4,5,7,1,2,8,3,6,10,9,12,11] => [8,5,4,3,2,7,6,1,10,9,12,11] => 11110110101
[(1,4),(2,5),(3,7),(6,8),(9,11),(10,12)] => [4,5,7,1,2,8,3,6,11,12,9,10] => [8,5,4,3,2,7,6,1,12,11,10,9] => 11110110111
[(1,4),(2,5),(3,7),(6,9),(8,10),(11,12)] => [4,5,7,1,2,9,3,10,6,8,12,11] => [10,5,4,3,2,7,6,9,8,1,12,11] => 11110101101
[(1,4),(2,5),(3,7),(6,9),(8,11),(10,12)] => [4,5,7,1,2,9,3,11,6,12,8,10] => [12,5,4,3,2,7,6,9,8,11,10,1] => 11110101011
[(1,4),(2,5),(3,7),(6,10),(8,11),(9,12)] => [4,5,7,1,2,10,3,11,12,6,8,9] => [12,5,4,3,2,7,6,11,10,9,8,1] => 11110101111
[(1,4),(2,5),(3,8),(6,9),(7,10),(11,12)] => [4,5,8,1,2,9,10,3,6,7,12,11] => [10,5,4,3,2,9,8,7,6,1,12,11] => 11110111101
[(1,4),(2,5),(3,8),(6,9),(7,11),(10,12)] => [4,5,8,1,2,9,11,3,6,12,7,10] => [12,5,4,3,2,9,8,7,6,11,10,1] => 11110111011
[(1,4),(2,5),(3,8),(6,10),(7,11),(9,12)] => [4,5,8,1,2,10,11,3,12,6,7,9] => [12,5,4,3,2,11,8,7,10,9,6,1] => 11110110111
[(1,4),(2,5),(3,9),(6,10),(7,11),(8,12)] => [4,5,9,1,2,10,11,12,3,6,7,8] => [12,5,4,3,2,11,10,9,8,7,6,1] => 11110111111
[(1,4),(2,6),(3,7),(5,8),(9,10),(11,12)] => [4,6,7,1,8,2,3,5,10,9,12,11] => [8,7,4,3,6,5,2,1,10,9,12,11] => 11101110101
[(1,4),(2,6),(3,7),(5,8),(9,11),(10,12)] => [4,6,7,1,8,2,3,5,11,12,9,10] => [8,7,4,3,6,5,2,1,12,11,10,9] => 11101110111
[(1,4),(2,6),(3,7),(5,9),(8,10),(11,12)] => [4,6,7,1,9,2,3,10,5,8,12,11] => [10,7,4,3,6,5,2,9,8,1,12,11] => 11101101101
[(1,4),(2,6),(3,7),(5,9),(8,11),(10,12)] => [4,6,7,1,9,2,3,11,5,12,8,10] => [12,7,4,3,6,5,2,9,8,11,10,1] => 11101101011
[(1,4),(2,6),(3,7),(5,10),(8,11),(9,12)] => [4,6,7,1,10,2,3,11,12,5,8,9] => [12,7,4,3,6,5,2,11,10,9,8,1] => 11101101111
[(1,4),(2,6),(3,8),(5,9),(7,10),(11,12)] => [4,6,8,1,9,2,10,3,5,7,12,11] => [10,9,4,3,6,5,8,7,2,1,12,11] => 11101011101
[(1,4),(2,6),(3,8),(5,9),(7,11),(10,12)] => [4,6,8,1,9,2,11,3,5,12,7,10] => [12,9,4,3,6,5,8,7,2,11,10,1] => 11101011011
[(1,4),(2,6),(3,8),(5,10),(7,11),(9,12)] => [4,6,8,1,10,2,11,3,12,5,7,9] => [12,11,4,3,6,5,8,7,10,9,2,1] => 11101010111
[(1,4),(2,6),(3,9),(5,10),(7,11),(8,12)] => [4,6,9,1,10,2,11,12,3,5,7,8] => [12,11,4,3,6,5,10,9,8,7,2,1] => 11101011111
[(1,4),(2,7),(3,8),(5,9),(6,10),(11,12)] => [4,7,8,1,9,10,2,3,5,6,12,11] => [10,9,4,3,8,7,6,5,2,1,12,11] => 11101111101
[(1,4),(2,7),(3,8),(5,9),(6,11),(10,12)] => [4,7,8,1,9,11,2,3,5,12,6,10] => [12,9,4,3,8,7,6,5,2,11,10,1] => 11101111011
[(1,4),(2,7),(3,8),(5,10),(6,11),(9,12)] => [4,7,8,1,10,11,2,3,12,5,6,9] => [12,11,4,3,8,7,6,5,10,9,2,1] => 11101110111
[(1,4),(2,7),(3,9),(5,10),(6,11),(8,12)] => [4,7,9,1,10,11,2,12,3,5,6,8] => [12,11,4,3,10,7,6,9,8,5,2,1] => 11101101111
[(1,4),(2,8),(3,9),(5,10),(6,11),(7,12)] => [4,8,9,1,10,11,12,2,3,5,6,7] => [12,11,4,3,10,9,8,7,6,5,2,1] => 11101111111
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [8,7,6,5,4,3,2,1,10,9,12,11] => 11111110101
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [8,7,6,5,4,3,2,1,12,11,10,9] => 11111110111
[(1,5),(2,6),(3,7),(4,9),(8,10),(11,12)] => [5,6,7,9,1,2,3,10,4,8,12,11] => [10,7,6,5,4,3,2,9,8,1,12,11] => 11111101101
[(1,5),(2,6),(3,7),(4,9),(8,11),(10,12)] => [5,6,7,9,1,2,3,11,4,12,8,10] => [12,7,6,5,4,3,2,9,8,11,10,1] => 11111101011
[(1,5),(2,6),(3,7),(4,10),(8,11),(9,12)] => [5,6,7,10,1,2,3,11,12,4,8,9] => [12,7,6,5,4,3,2,11,10,9,8,1] => 11111101111
[(1,5),(2,6),(3,8),(4,9),(7,10),(11,12)] => [5,6,8,9,1,2,10,3,4,7,12,11] => [10,9,6,5,4,3,8,7,2,1,12,11] => 11111011101
[(1,5),(2,6),(3,8),(4,9),(7,11),(10,12)] => [5,6,8,9,1,2,11,3,4,12,7,10] => [12,9,6,5,4,3,8,7,2,11,10,1] => 11111011011
[(1,5),(2,6),(3,8),(4,10),(7,11),(9,12)] => [5,6,8,10,1,2,11,3,12,4,7,9] => [12,11,6,5,4,3,8,7,10,9,2,1] => 11111010111
[(1,5),(2,6),(3,9),(4,10),(7,11),(8,12)] => [5,6,9,10,1,2,11,12,3,4,7,8] => [12,11,6,5,4,3,10,9,8,7,2,1] => 11111011111
[(1,5),(2,7),(3,8),(4,9),(6,10),(11,12)] => [5,7,8,9,1,10,2,3,4,6,12,11] => [10,9,8,5,4,7,6,3,2,1,12,11] => 11110111101
[(1,5),(2,7),(3,8),(4,9),(6,11),(10,12)] => [5,7,8,9,1,11,2,3,4,12,6,10] => [12,9,8,5,4,7,6,3,2,11,10,1] => 11110111011
[(1,5),(2,7),(3,8),(4,10),(6,11),(9,12)] => [5,7,8,10,1,11,2,3,12,4,6,9] => [12,11,8,5,4,7,6,3,10,9,2,1] => 11110110111
[(1,5),(2,7),(3,9),(4,10),(6,11),(8,12)] => [5,7,9,10,1,11,2,12,3,4,6,8] => [12,11,10,5,4,7,6,9,8,3,2,1] => 11110101111
[(1,5),(2,8),(3,9),(4,10),(6,11),(7,12)] => [5,8,9,10,1,11,12,2,3,4,6,7] => [12,11,10,5,4,9,8,7,6,3,2,1] => 11110111111
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [10,9,8,7,6,5,4,3,2,1,12,11] => 11111111101
[(1,6),(2,7),(3,8),(4,9),(5,11),(10,12)] => [6,7,8,9,11,1,2,3,4,12,5,10] => [12,9,8,7,6,5,4,3,2,11,10,1] => 11111111011
[(1,6),(2,7),(3,8),(4,10),(5,11),(9,12)] => [6,7,8,10,11,1,2,3,12,4,5,9] => [12,11,8,7,6,5,4,3,10,9,2,1] => 11111110111
[(1,6),(2,7),(3,9),(4,10),(5,11),(8,12)] => [6,7,9,10,11,1,2,12,3,4,5,8] => [12,11,10,7,6,5,4,9,8,3,2,1] => 11111101111
[(1,6),(2,8),(3,9),(4,10),(5,11),(7,12)] => [6,8,9,10,11,1,12,2,3,4,5,7] => [12,11,10,9,6,5,8,7,4,3,2,1] => 11111011111
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,11,10,9,8,7,6,5,4,3,2,1] => 11111111111
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
Map
descent word
Description
The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.