Identifier
Mp00058: Perfect matchings to permutationPermutations
Mp00237: Permutations descent views to invisible inversion bottomsPermutations
Mp00109: Permutations descent wordBinary 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] => 101
[(1,4),(2,3)] => [4,3,2,1] => [2,3,4,1] => 001
[(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] => 10101
[(1,4),(2,3),(5,6)] => [4,3,2,1,6,5] => [2,3,4,1,6,5] => 00101
[(1,5),(2,3),(4,6)] => [5,3,2,6,1,4] => [6,3,5,1,2,4] => 10100
[(1,6),(2,3),(4,5)] => [6,3,2,5,4,1] => [4,3,5,6,1,2] => 10010
[(1,6),(2,4),(3,5)] => [6,4,5,2,3,1] => [3,5,2,6,4,1] => 01011
[(1,5),(2,4),(3,6)] => [5,4,6,2,1,3] => [2,6,1,5,4,3] => 01011
[(1,4),(2,5),(3,6)] => [4,5,6,1,2,3] => [6,1,2,4,5,3] => 10001
[(1,3),(2,5),(4,6)] => [3,5,1,6,2,4] => [5,6,3,2,1,4] => 01110
[(1,2),(3,5),(4,6)] => [2,1,5,6,3,4] => [2,1,6,3,5,4] => 10101
[(1,2),(3,6),(4,5)] => [2,1,6,5,4,3] => [2,1,4,5,6,3] => 10001
[(1,3),(2,6),(4,5)] => [3,6,1,5,4,2] => [6,4,3,5,1,2] => 11010
[(1,4),(2,6),(3,5)] => [4,6,5,1,3,2] => [5,3,1,4,6,2] => 11001
[(1,5),(2,6),(3,4)] => [5,6,4,3,1,2] => [3,1,4,6,5,2] => 10011
[(1,6),(2,5),(3,4)] => [6,5,4,3,2,1] => [2,3,4,5,6,1] => 00001
[(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] => 1010101
[(1,4),(2,3),(5,6),(7,8)] => [4,3,2,1,6,5,8,7] => [2,3,4,1,6,5,8,7] => 0010101
[(1,5),(2,3),(4,6),(7,8)] => [5,3,2,6,1,4,8,7] => [6,3,5,1,2,4,8,7] => 1010001
[(1,6),(2,3),(4,5),(7,8)] => [6,3,2,5,4,1,8,7] => [4,3,5,6,1,2,8,7] => 1001001
[(1,7),(2,3),(4,5),(6,8)] => [7,3,2,5,4,8,1,6] => [8,3,7,5,2,1,4,6] => 1011100
[(1,8),(2,3),(4,5),(6,7)] => [8,3,2,5,4,7,6,1] => [6,3,7,5,2,8,1,4] => 1011010
[(1,8),(2,4),(3,5),(6,7)] => [8,4,5,2,3,7,6,1] => [6,5,2,7,4,8,1,3] => 1101010
[(1,7),(2,4),(3,5),(6,8)] => [7,4,5,2,3,8,1,6] => [8,5,2,7,4,1,3,6] => 1101100
[(1,6),(2,4),(3,5),(7,8)] => [6,4,5,2,3,1,8,7] => [3,5,2,6,4,1,8,7] => 0101101
[(1,5),(2,4),(3,6),(7,8)] => [5,4,6,2,1,3,8,7] => [2,6,1,5,4,3,8,7] => 0101101
[(1,4),(2,5),(3,6),(7,8)] => [4,5,6,1,2,3,8,7] => [6,1,2,4,5,3,8,7] => 1000101
[(1,3),(2,5),(4,6),(7,8)] => [3,5,1,6,2,4,8,7] => [5,6,3,2,1,4,8,7] => 0111001
[(1,2),(3,5),(4,6),(7,8)] => [2,1,5,6,3,4,8,7] => [2,1,6,3,5,4,8,7] => 1010101
[(1,2),(3,6),(4,5),(7,8)] => [2,1,6,5,4,3,8,7] => [2,1,4,5,6,3,8,7] => 1000101
[(1,3),(2,6),(4,5),(7,8)] => [3,6,1,5,4,2,8,7] => [6,4,3,5,1,2,8,7] => 1101001
[(1,4),(2,6),(3,5),(7,8)] => [4,6,5,1,3,2,8,7] => [5,3,1,4,6,2,8,7] => 1100101
[(1,5),(2,6),(3,4),(7,8)] => [5,6,4,3,1,2,8,7] => [3,1,4,6,5,2,8,7] => 1001101
[(1,6),(2,5),(3,4),(7,8)] => [6,5,4,3,2,1,8,7] => [2,3,4,5,6,1,8,7] => 0000101
[(1,7),(2,5),(3,4),(6,8)] => [7,5,4,3,2,8,1,6] => [8,3,4,5,7,1,2,6] => 1000100
[(1,8),(2,5),(3,4),(6,7)] => [8,5,4,3,2,7,6,1] => [6,3,4,5,7,8,1,2] => 1000010
[(1,8),(2,6),(3,4),(5,7)] => [8,6,4,3,7,2,5,1] => [5,7,4,6,2,8,3,1] => 0101011
[(1,7),(2,6),(3,4),(5,8)] => [7,6,4,3,8,2,1,5] => [2,8,4,6,1,7,3,5] => 0101010
[(1,6),(2,7),(3,4),(5,8)] => [6,7,4,3,8,1,2,5] => [8,1,4,7,2,6,3,5] => 1001010
[(1,5),(2,7),(3,4),(6,8)] => [5,7,4,3,1,8,2,6] => [3,4,7,8,5,2,1,6] => 0001110
[(1,4),(2,7),(3,5),(6,8)] => [4,7,5,1,3,8,2,6] => [5,7,1,4,8,3,2,6] => 0100110
[(1,3),(2,7),(4,5),(6,8)] => [3,7,1,5,4,8,2,6] => [7,8,3,5,1,4,6,2] => 0101001
[(1,2),(3,7),(4,5),(6,8)] => [2,1,7,5,4,8,3,6] => [2,1,8,5,7,3,4,6] => 1010100
[(1,2),(3,8),(4,5),(6,7)] => [2,1,8,5,4,7,6,3] => [2,1,6,5,7,8,3,4] => 1010010
[(1,3),(2,8),(4,5),(6,7)] => [3,8,1,5,4,7,6,2] => [8,6,3,5,1,7,4,2] => 1101011
[(1,4),(2,8),(3,5),(6,7)] => [4,8,5,1,3,7,6,2] => [5,8,1,4,6,7,2,3] => 0100010
[(1,5),(2,8),(3,4),(6,7)] => [5,8,4,3,1,7,6,2] => [3,4,8,6,5,7,1,2] => 0011010
[(1,6),(2,8),(3,4),(5,7)] => [6,8,4,3,7,1,5,2] => [7,5,4,8,1,6,3,2] => 1101011
[(1,7),(2,8),(3,4),(5,6)] => [7,8,4,3,6,5,1,2] => [5,1,4,6,8,2,7,3] => 1000101
[(1,8),(2,7),(3,4),(5,6)] => [8,7,4,3,6,5,2,1] => [2,5,4,6,7,1,8,3] => 0100101
[(1,8),(2,7),(3,5),(4,6)] => [8,7,5,6,3,4,2,1] => [2,4,6,3,7,5,8,1] => 0010101
[(1,7),(2,8),(3,5),(4,6)] => [7,8,5,6,3,4,1,2] => [4,1,6,3,8,5,7,2] => 1010101
[(1,6),(2,8),(3,5),(4,7)] => [6,8,5,7,3,1,4,2] => [3,7,4,2,8,6,5,1] => 0110111
[(1,5),(2,8),(3,6),(4,7)] => [5,8,6,7,1,3,4,2] => [7,4,1,3,5,8,6,2] => 1100011
[(1,4),(2,8),(3,6),(5,7)] => [4,8,6,1,7,3,5,2] => [6,5,8,4,3,7,2,1] => 1011011
[(1,3),(2,8),(4,6),(5,7)] => [3,8,1,6,7,4,5,2] => [8,5,3,7,4,1,6,2] => 1101101
[(1,2),(3,8),(4,6),(5,7)] => [2,1,8,6,7,4,5,3] => [2,1,5,7,4,8,6,3] => 1001011
[(1,2),(3,7),(4,6),(5,8)] => [2,1,7,6,8,4,3,5] => [2,1,4,8,3,7,6,5] => 1001011
[(1,3),(2,7),(4,6),(5,8)] => [3,7,1,6,8,4,2,5] => [7,4,3,8,2,1,6,5] => 1101101
[(1,4),(2,7),(3,6),(5,8)] => [4,7,6,1,8,3,2,5] => [6,3,7,4,2,8,5,1] => 1011011
[(1,5),(2,7),(3,6),(4,8)] => [5,7,6,8,1,3,2,4] => [8,3,1,2,5,7,6,4] => 1100011
[(1,6),(2,7),(3,5),(4,8)] => [6,7,5,8,3,1,2,4] => [3,1,8,2,7,6,5,4] => 1010111
[(1,7),(2,6),(3,5),(4,8)] => [7,6,5,8,3,2,1,4] => [2,3,8,1,6,7,5,4] => 0010011
[(1,8),(2,6),(3,5),(4,7)] => [8,6,5,7,3,2,4,1] => [4,3,7,2,6,8,5,1] => 1010011
[(1,8),(2,5),(3,6),(4,7)] => [8,5,6,7,2,3,4,1] => [4,7,2,3,8,5,6,1] => 0100101
[(1,7),(2,5),(3,6),(4,8)] => [7,5,6,8,2,3,1,4] => [3,8,2,1,7,5,6,4] => 0110101
[(1,6),(2,5),(3,7),(4,8)] => [6,5,7,8,2,1,3,4] => [2,8,1,3,6,5,7,4] => 0100101
[(1,5),(2,6),(3,7),(4,8)] => [5,6,7,8,1,2,3,4] => [8,1,2,3,5,6,7,4] => 1000001
[(1,4),(2,6),(3,7),(5,8)] => [4,6,7,1,8,2,3,5] => [7,8,2,4,3,6,1,5] => 0101010
[(1,3),(2,6),(4,7),(5,8)] => [3,6,1,7,8,2,4,5] => [6,8,3,2,4,1,7,5] => 0110101
[(1,2),(3,6),(4,7),(5,8)] => [2,1,6,7,8,3,4,5] => [2,1,8,3,4,6,7,5] => 1010001
[(1,2),(3,5),(4,7),(6,8)] => [2,1,5,7,3,8,4,6] => [2,1,7,8,5,4,3,6] => 1001110
[(1,3),(2,5),(4,7),(6,8)] => [3,5,1,7,2,8,4,6] => [5,7,3,8,1,4,2,6] => 0101010
[(1,4),(2,5),(3,7),(6,8)] => [4,5,7,1,2,8,3,6] => [7,1,8,4,5,3,2,6] => 1010110
[(1,5),(2,4),(3,7),(6,8)] => [5,4,7,2,1,8,3,6] => [2,7,8,5,4,3,1,6] => 0011110
[(1,6),(2,4),(3,7),(5,8)] => [6,4,7,2,8,1,3,5] => [8,7,1,6,2,4,5,3] => 1101001
[(1,7),(2,4),(3,6),(5,8)] => [7,4,6,2,8,3,1,5] => [3,8,6,7,1,4,5,2] => 0101001
[(1,8),(2,4),(3,6),(5,7)] => [8,4,6,2,7,3,5,1] => [5,6,7,8,3,4,2,1] => 0001011
[(1,8),(2,3),(4,6),(5,7)] => [8,3,2,6,7,4,5,1] => [5,3,8,7,4,1,2,6] => 1011100
[(1,7),(2,3),(4,6),(5,8)] => [7,3,2,6,8,4,1,5] => [4,3,8,7,1,5,6,2] => 1011001
[(1,6),(2,3),(4,7),(5,8)] => [6,3,2,7,8,1,4,5] => [8,3,6,1,2,5,7,4] => 1010001
[(1,5),(2,3),(4,7),(6,8)] => [5,3,2,7,1,8,4,6] => [7,3,5,8,2,4,1,6] => 1001010
[(1,4),(2,3),(5,7),(6,8)] => [4,3,2,1,7,8,5,6] => [2,3,4,1,8,5,7,6] => 0010101
[(1,3),(2,4),(5,7),(6,8)] => [3,4,1,2,7,8,5,6] => [4,1,3,2,8,5,7,6] => 1010101
[(1,2),(3,4),(5,7),(6,8)] => [2,1,4,3,7,8,5,6] => [2,1,4,3,8,5,7,6] => 1010101
[(1,2),(3,4),(5,8),(6,7)] => [2,1,4,3,8,7,6,5] => [2,1,4,3,6,7,8,5] => 1010001
[(1,3),(2,4),(5,8),(6,7)] => [3,4,1,2,8,7,6,5] => [4,1,3,2,6,7,8,5] => 1010001
[(1,4),(2,3),(5,8),(6,7)] => [4,3,2,1,8,7,6,5] => [2,3,4,1,6,7,8,5] => 0010001
[(1,5),(2,3),(4,8),(6,7)] => [5,3,2,8,1,7,6,4] => [8,3,5,6,2,7,1,4] => 1001010
[(1,6),(2,3),(4,8),(5,7)] => [6,3,2,8,7,1,5,4] => [7,3,6,5,1,2,8,4] => 1011001
[(1,7),(2,3),(4,8),(5,6)] => [7,3,2,8,6,5,1,4] => [5,3,6,1,8,7,2,4] => 1010110
[(1,8),(2,3),(4,7),(5,6)] => [8,3,2,7,6,5,4,1] => [4,3,5,6,7,8,1,2] => 1000010
[(1,8),(2,4),(3,7),(5,6)] => [8,4,7,2,6,5,3,1] => [3,5,6,7,8,2,1,4] => 0000110
[(1,7),(2,4),(3,8),(5,6)] => [7,4,8,2,6,5,1,3] => [5,6,1,8,7,3,2,4] => 0101110
[(1,6),(2,4),(3,8),(5,7)] => [6,4,8,2,7,1,5,3] => [7,8,5,6,1,4,2,3] => 0101010
[(1,5),(2,4),(3,8),(6,7)] => [5,4,8,2,1,7,6,3] => [2,8,6,5,4,7,1,3] => 0111010
[(1,4),(2,5),(3,8),(6,7)] => [4,5,8,1,2,7,6,3] => [8,1,6,4,5,7,2,3] => 1010010
>>> Load all 290 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [3,5,1,8,2,7,6,4] => [5,8,3,6,1,7,2,4] => 0101010
[(1,2),(3,5),(4,8),(6,7)] => [2,1,5,8,3,7,6,4] => [2,1,8,6,5,7,3,4] => 1011010
[(1,2),(3,6),(4,8),(5,7)] => [2,1,6,8,7,3,5,4] => [2,1,7,5,3,6,8,4] => 1011001
[(1,3),(2,6),(4,8),(5,7)] => [3,6,1,8,7,2,5,4] => [6,7,3,5,2,1,8,4] => 0101101
[(1,4),(2,6),(3,8),(5,7)] => [4,6,8,1,7,2,5,3] => [8,7,5,4,2,6,1,3] => 1111010
[(1,5),(2,6),(3,8),(4,7)] => [5,6,8,7,1,2,4,3] => [7,1,4,2,5,6,8,3] => 1010001
[(1,6),(2,5),(3,8),(4,7)] => [6,5,8,7,2,1,4,3] => [2,7,4,1,6,5,8,3] => 0110101
[(1,7),(2,5),(3,8),(4,6)] => [7,5,8,6,2,4,1,3] => [4,6,1,2,8,7,3,5] => 0100110
[(1,8),(2,5),(3,7),(4,6)] => [8,5,7,6,2,4,3,1] => [3,4,6,1,7,8,2,5] => 0010010
[(1,8),(2,6),(3,7),(4,5)] => [8,6,7,5,4,2,3,1] => [3,4,2,5,7,8,6,1] => 0100011
[(1,7),(2,6),(3,8),(4,5)] => [7,6,8,5,4,2,1,3] => [2,4,1,5,8,7,6,3] => 0100111
[(1,6),(2,7),(3,8),(4,5)] => [6,7,8,5,4,1,2,3] => [4,1,2,5,8,6,7,3] => 1000101
[(1,5),(2,7),(3,8),(4,6)] => [5,7,8,6,1,4,2,3] => [6,4,2,1,5,8,7,3] => 1110011
[(1,4),(2,7),(3,8),(5,6)] => [4,7,8,1,6,5,2,3] => [8,5,2,4,6,1,7,3] => 1100101
[(1,3),(2,7),(4,8),(5,6)] => [3,7,1,8,6,5,2,4] => [7,5,3,2,6,8,1,4] => 1110010
[(1,2),(3,7),(4,8),(5,6)] => [2,1,7,8,6,5,3,4] => [2,1,5,3,6,8,7,4] => 1010011
[(1,2),(3,8),(4,7),(5,6)] => [2,1,8,7,6,5,4,3] => [2,1,4,5,6,7,8,3] => 1000001
[(1,3),(2,8),(4,7),(5,6)] => [3,8,1,7,6,5,4,2] => [8,4,3,5,6,7,1,2] => 1100010
[(1,4),(2,8),(3,7),(5,6)] => [4,8,7,1,6,5,3,2] => [7,3,5,4,6,1,8,2] => 1010101
[(1,5),(2,8),(3,7),(4,6)] => [5,8,7,6,1,4,3,2] => [6,3,4,1,5,7,8,2] => 1010001
[(1,6),(2,8),(3,7),(4,5)] => [6,8,7,5,4,1,3,2] => [4,3,1,5,7,6,8,2] => 1100101
[(1,7),(2,8),(3,6),(4,5)] => [7,8,6,5,4,3,1,2] => [3,1,4,5,6,8,7,2] => 1000011
[(1,8),(2,7),(3,6),(4,5)] => [8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,1] => 0000001
[(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] => 101010101
[(1,4),(2,3),(5,6),(7,8),(9,10)] => [4,3,2,1,6,5,8,7,10,9] => [2,3,4,1,6,5,8,7,10,9] => 001010101
[(1,6),(2,3),(4,5),(7,8),(9,10)] => [6,3,2,5,4,1,8,7,10,9] => [4,3,5,6,1,2,8,7,10,9] => 100100101
[(1,4),(2,5),(3,6),(7,8),(9,10)] => [4,5,6,1,2,3,8,7,10,9] => [6,1,2,4,5,3,8,7,10,9] => 100010101
[(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] => 101010101
[(1,2),(3,6),(4,5),(7,8),(9,10)] => [2,1,6,5,4,3,8,7,10,9] => [2,1,4,5,6,3,8,7,10,9] => 100010101
[(1,6),(2,5),(3,4),(7,8),(9,10)] => [6,5,4,3,2,1,8,7,10,9] => [2,3,4,5,6,1,8,7,10,9] => 000010101
[(1,8),(2,5),(3,4),(6,7),(9,10)] => [8,5,4,3,2,7,6,1,10,9] => [6,3,4,5,7,8,1,2,10,9] => 100001001
[(1,2),(3,8),(4,5),(6,7),(9,10)] => [2,1,8,5,4,7,6,3,10,9] => [2,1,6,5,7,8,3,4,10,9] => 101001001
[(1,8),(2,7),(3,4),(5,6),(9,10)] => [8,7,4,3,6,5,2,1,10,9] => [2,5,4,6,7,1,8,3,10,9] => 010010101
[(1,8),(2,9),(3,5),(4,6),(7,10)] => [8,9,5,6,3,4,10,1,2,7] => [10,1,6,3,9,5,2,8,4,7] => 101011010
[(1,5),(2,6),(3,7),(4,8),(9,10)] => [5,6,7,8,1,2,3,4,10,9] => [8,1,2,3,5,6,7,4,10,9] => 100000101
[(1,2),(3,6),(4,7),(5,8),(9,10)] => [2,1,6,7,8,3,4,5,10,9] => [2,1,8,3,4,6,7,5,10,9] => 101000101
[(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] => 101010101
[(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] => 101010101
[(1,2),(3,4),(5,8),(6,7),(9,10)] => [2,1,4,3,8,7,6,5,10,9] => [2,1,4,3,6,7,8,5,10,9] => 101000101
[(1,4),(2,3),(5,8),(6,7),(9,10)] => [4,3,2,1,8,7,6,5,10,9] => [2,3,4,1,6,7,8,5,10,9] => 001000101
[(1,8),(2,3),(4,7),(5,6),(9,10)] => [8,3,2,7,6,5,4,1,10,9] => [4,3,5,6,7,8,1,2,10,9] => 100001001
[(1,2),(3,8),(4,7),(5,6),(9,10)] => [2,1,8,7,6,5,4,3,10,9] => [2,1,4,5,6,7,8,3,10,9] => 100000101
[(1,8),(2,7),(3,6),(4,5),(9,10)] => [8,7,6,5,4,3,2,1,10,9] => [2,3,4,5,6,7,8,1,10,9] => 000000101
[(1,9),(2,7),(3,6),(4,5),(8,10)] => [9,7,6,5,4,3,2,10,1,8] => [10,3,4,5,6,7,9,1,2,8] => 100000100
[(1,10),(2,7),(3,6),(4,5),(8,9)] => [10,7,6,5,4,3,2,9,8,1] => [8,3,4,5,6,7,9,10,1,2] => 100000010
[(1,2),(3,10),(4,7),(5,6),(8,9)] => [2,1,10,7,6,5,4,9,8,3] => [2,1,8,5,6,7,9,10,3,4] => 101000010
[(1,10),(2,9),(3,6),(4,5),(7,8)] => [10,9,6,5,4,3,8,7,2,1] => [2,7,4,5,6,8,9,1,10,3] => 010000101
[(1,2),(3,4),(5,10),(6,7),(8,9)] => [2,1,4,3,10,7,6,9,8,5] => [2,1,4,3,8,7,9,10,5,6] => 101010010
[(1,4),(2,3),(5,10),(6,7),(8,9)] => [4,3,2,1,10,7,6,9,8,5] => [2,3,4,1,8,7,9,10,5,6] => 001010010
[(1,2),(3,10),(4,9),(5,6),(7,8)] => [2,1,10,9,6,5,8,7,4,3] => [2,1,4,7,6,8,9,3,10,5] => 100100101
[(1,10),(2,9),(3,8),(4,5),(6,7)] => [10,9,8,5,4,7,6,3,2,1] => [2,3,6,5,7,8,1,9,10,4] => 001001001
[(1,10),(2,8),(3,9),(4,6),(5,7)] => [10,8,9,6,7,4,5,2,3,1] => [3,5,2,7,4,9,6,10,8,1] => 010101011
[(1,2),(3,7),(4,8),(5,9),(6,10)] => [2,1,7,8,9,10,3,4,5,6] => [2,1,10,3,4,5,7,8,9,6] => 101000001
[(1,6),(2,7),(3,8),(4,9),(5,10)] => [6,7,8,9,10,1,2,3,4,5] => [10,1,2,3,4,6,7,8,9,5] => 100000001
[(1,3),(2,4),(5,8),(6,9),(7,10)] => [3,4,1,2,8,9,10,5,6,7] => [4,1,3,2,10,5,6,8,9,7] => 101010001
[(1,2),(3,4),(5,8),(6,9),(7,10)] => [2,1,4,3,8,9,10,5,6,7] => [2,1,4,3,10,5,6,8,9,7] => 101010001
[(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] => 101010101
[(1,4),(2,5),(3,6),(7,9),(8,10)] => [4,5,6,1,2,3,9,10,7,8] => [6,1,2,4,5,3,10,7,9,8] => 100010101
[(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] => 101010101
[(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] => 101010101
[(1,2),(3,4),(5,6),(7,10),(8,9)] => [2,1,4,3,6,5,10,9,8,7] => [2,1,4,3,6,5,8,9,10,7] => 101010001
[(1,4),(2,3),(5,6),(7,10),(8,9)] => [4,3,2,1,6,5,10,9,8,7] => [2,3,4,1,6,5,8,9,10,7] => 001010001
[(1,6),(2,3),(4,5),(7,10),(8,9)] => [6,3,2,5,4,1,10,9,8,7] => [4,3,5,6,1,2,8,9,10,7] => 100100001
[(1,2),(3,6),(4,5),(7,10),(8,9)] => [2,1,6,5,4,3,10,9,8,7] => [2,1,4,5,6,3,8,9,10,7] => 100010001
[(1,6),(2,5),(3,4),(7,10),(8,9)] => [6,5,4,3,2,1,10,9,8,7] => [2,3,4,5,6,1,8,9,10,7] => 000010001
[(1,10),(2,5),(3,4),(6,9),(7,8)] => [10,5,4,3,2,9,8,7,6,1] => [6,3,4,5,7,8,9,10,1,2] => 100000010
[(1,2),(3,10),(4,5),(6,9),(7,8)] => [2,1,10,5,4,9,8,7,6,3] => [2,1,6,5,7,8,9,10,3,4] => 101000010
[(1,10),(2,9),(3,4),(5,8),(6,7)] => [10,9,4,3,8,7,6,5,2,1] => [2,5,4,6,7,8,9,1,10,3] => 010000101
[(1,9),(2,7),(3,5),(4,10),(6,8)] => [9,7,5,10,3,8,2,6,1,4] => [6,8,10,1,7,2,9,3,5,4] => 001010101
[(1,2),(3,4),(5,10),(6,9),(7,8)] => [2,1,4,3,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,5] => 101000001
[(1,4),(2,3),(5,10),(6,9),(7,8)] => [4,3,2,1,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,5] => 001000001
[(1,10),(2,3),(4,9),(5,8),(6,7)] => [10,3,2,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,1,2] => 100000010
[(1,2),(3,10),(4,9),(5,8),(6,7)] => [2,1,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,3] => 100000001
[(1,10),(2,9),(3,8),(4,7),(5,6)] => [10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,1] => 000000001
[(1,12),(2,11),(3,10),(4,9),(5,8),(6,7)] => [12,11,10,9,8,7,6,5,4,3,2,1] => [2,3,4,5,6,7,8,9,10,11,12,1] => 00000000001
[(1,2),(3,10),(4,9),(5,8),(6,7),(11,12)] => [2,1,10,9,8,7,6,5,4,3,12,11] => [2,1,4,5,6,7,8,9,10,3,12,11] => 10000000101
[(1,2),(3,12),(4,9),(5,8),(6,7),(10,11)] => [2,1,12,9,8,7,6,5,4,11,10,3] => [2,1,10,5,6,7,8,9,11,12,3,4] => 10100000010
[(1,10),(2,3),(4,9),(5,8),(6,7),(11,12)] => [10,3,2,9,8,7,6,5,4,1,12,11] => [4,3,5,6,7,8,9,10,1,2,12,11] => 10000001001
[(1,2),(3,4),(5,8),(6,7),(9,10),(11,12)] => [2,1,4,3,8,7,6,5,10,9,12,11] => [2,1,4,3,6,7,8,5,10,9,12,11] => 10100010101
[(1,2),(3,12),(4,11),(5,8),(6,7),(9,10)] => [2,1,12,11,8,7,6,5,10,9,4,3] => [2,1,4,9,6,7,8,10,11,3,12,5] => 10010000101
[(1,4),(2,3),(5,8),(6,7),(9,10),(11,12)] => [4,3,2,1,8,7,6,5,10,9,12,11] => [2,3,4,1,6,7,8,5,10,9,12,11] => 00100010101
[(1,2),(3,4),(5,8),(6,7),(9,12),(10,11)] => [2,1,4,3,8,7,6,5,12,11,10,9] => [2,1,4,3,6,7,8,5,10,11,12,9] => 10100010001
[(1,10),(2,9),(3,4),(5,8),(6,7),(11,12)] => [10,9,4,3,8,7,6,5,2,1,12,11] => [2,5,4,6,7,8,9,1,10,3,12,11] => 01000010101
[(1,4),(2,3),(5,8),(6,7),(9,12),(10,11)] => [4,3,2,1,8,7,6,5,12,11,10,9] => [2,3,4,1,6,7,8,5,10,11,12,9] => 00100010001
[(1,2),(3,4),(5,10),(6,7),(8,9),(11,12)] => [2,1,4,3,10,7,6,9,8,5,12,11] => [2,1,4,3,8,7,9,10,5,6,12,11] => 10101001001
[(1,2),(3,12),(4,11),(5,10),(6,7),(8,9)] => [2,1,12,11,10,7,6,9,8,5,4,3] => [2,1,4,5,8,7,9,10,3,11,12,6] => 10001001001
[(1,4),(2,3),(5,10),(6,7),(8,9),(11,12)] => [4,3,2,1,10,7,6,9,8,5,12,11] => [2,3,4,1,8,7,9,10,5,6,12,11] => 00101001001
[(1,2),(3,8),(4,5),(6,7),(9,10),(11,12)] => [2,1,8,5,4,7,6,3,10,9,12,11] => [2,1,6,5,7,8,3,4,10,9,12,11] => 10100100101
[(1,2),(3,8),(4,5),(6,7),(9,12),(10,11)] => [2,1,8,5,4,7,6,3,12,11,10,9] => [2,1,6,5,7,8,3,4,10,11,12,9] => 10100100001
[(1,10),(2,9),(3,8),(4,5),(6,7),(11,12)] => [10,9,8,5,4,7,6,3,2,1,12,11] => [2,3,6,5,7,8,1,9,10,4,12,11] => 00100100101
[(1,2),(3,4),(5,12),(6,7),(8,11),(9,10)] => [2,1,4,3,12,7,6,11,10,9,8,5] => [2,1,4,3,8,7,9,10,11,12,5,6] => 10101000010
[(1,8),(2,5),(3,4),(6,7),(9,10),(11,12)] => [8,5,4,3,2,7,6,1,10,9,12,11] => [6,3,4,5,7,8,1,2,10,9,12,11] => 10000100101
[(1,4),(2,3),(5,12),(6,7),(8,11),(9,10)] => [4,3,2,1,12,7,6,11,10,9,8,5] => [2,3,4,1,8,7,9,10,11,12,5,6] => 00101000010
[(1,8),(2,5),(3,4),(6,7),(9,12),(10,11)] => [8,5,4,3,2,7,6,1,12,11,10,9] => [6,3,4,5,7,8,1,2,10,11,12,9] => 10000100001
[(1,12),(2,11),(3,10),(4,9),(5,6),(7,8)] => [12,11,10,9,6,5,8,7,4,3,2,1] => [2,3,4,7,6,8,9,1,10,11,12,5] => 00010010001
[(1,2),(3,10),(4,9),(5,6),(7,8),(11,12)] => [2,1,10,9,6,5,8,7,4,3,12,11] => [2,1,4,7,6,8,9,3,10,5,12,11] => 10010010101
[(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
[(1,4),(2,3),(5,6),(7,8),(9,10),(11,12)] => [4,3,2,1,6,5,8,7,10,9,12,11] => [2,3,4,1,6,5,8,7,10,9,12,11] => 00101010101
[(1,2),(3,4),(5,6),(7,8),(9,12),(10,11)] => [2,1,4,3,6,5,8,7,12,11,10,9] => [2,1,4,3,6,5,8,7,10,11,12,9] => 10101010001
[(1,4),(2,3),(5,6),(7,8),(9,12),(10,11)] => [4,3,2,1,6,5,8,7,12,11,10,9] => [2,3,4,1,6,5,8,7,10,11,12,9] => 00101010001
[(1,12),(2,11),(3,10),(4,5),(6,9),(7,8)] => [12,11,10,5,4,9,8,7,6,3,2,1] => [2,3,6,5,7,8,9,10,1,11,12,4] => 00100001001
[(1,2),(3,10),(4,5),(6,9),(7,8),(11,12)] => [2,1,10,5,4,9,8,7,6,3,12,11] => [2,1,6,5,7,8,9,10,3,4,12,11] => 10100001001
[(1,12),(2,11),(3,4),(5,10),(6,9),(7,8)] => [12,11,4,3,10,9,8,7,6,5,2,1] => [2,5,4,6,7,8,9,10,11,1,12,3] => 01000000101
[(1,2),(3,4),(5,10),(6,9),(7,8),(11,12)] => [2,1,4,3,10,9,8,7,6,5,12,11] => [2,1,4,3,6,7,8,9,10,5,12,11] => 10100000101
[(1,12),(2,3),(4,11),(5,10),(6,9),(7,8)] => [12,3,2,11,10,9,8,7,6,5,4,1] => [4,3,5,6,7,8,9,10,11,12,1,2] => 10000000010
[(1,2),(3,12),(4,11),(5,10),(6,9),(7,8)] => [2,1,12,11,10,9,8,7,6,5,4,3] => [2,1,4,5,6,7,8,9,10,11,12,3] => 10000000001
[(1,4),(2,3),(5,10),(6,9),(7,8),(11,12)] => [4,3,2,1,10,9,8,7,6,5,12,11] => [2,3,4,1,6,7,8,9,10,5,12,11] => 00100000101
[(1,2),(3,4),(5,12),(6,9),(7,8),(10,11)] => [2,1,4,3,12,9,8,7,6,11,10,5] => [2,1,4,3,10,7,8,9,11,12,5,6] => 10101000010
[(1,10),(2,5),(3,4),(6,9),(7,8),(11,12)] => [10,5,4,3,2,9,8,7,6,1,12,11] => [6,3,4,5,7,8,9,10,1,2,12,11] => 10000001001
[(1,4),(2,3),(5,12),(6,9),(7,8),(10,11)] => [4,3,2,1,12,9,8,7,6,11,10,5] => [2,3,4,1,10,7,8,9,11,12,5,6] => 00101000010
[(1,2),(3,6),(4,5),(7,8),(9,10),(11,12)] => [2,1,6,5,4,3,8,7,10,9,12,11] => [2,1,4,5,6,3,8,7,10,9,12,11] => 10001010101
[(1,6),(2,3),(4,5),(7,8),(9,10),(11,12)] => [6,3,2,5,4,1,8,7,10,9,12,11] => [4,3,5,6,1,2,8,7,10,9,12,11] => 10010010101
[(1,2),(3,6),(4,5),(7,8),(9,12),(10,11)] => [2,1,6,5,4,3,8,7,12,11,10,9] => [2,1,4,5,6,3,8,7,10,11,12,9] => 10001010001
[(1,10),(2,9),(3,6),(4,5),(7,8),(11,12)] => [10,9,6,5,4,3,8,7,2,1,12,11] => [2,7,4,5,6,8,9,1,10,3,12,11] => 01000010101
[(1,6),(2,3),(4,5),(7,8),(9,12),(10,11)] => [6,3,2,5,4,1,8,7,12,11,10,9] => [4,3,5,6,1,2,8,7,10,11,12,9] => 10010010001
[(1,2),(3,4),(5,12),(6,11),(7,8),(9,10)] => [2,1,4,3,12,11,8,7,10,9,6,5] => [2,1,4,3,6,9,8,10,11,5,12,7] => 10100100101
[(1,6),(2,5),(3,4),(7,8),(9,10),(11,12)] => [6,5,4,3,2,1,8,7,10,9,12,11] => [2,3,4,5,6,1,8,7,10,9,12,11] => 00001010101
[(1,4),(2,3),(5,12),(6,11),(7,8),(9,10)] => [4,3,2,1,12,11,8,7,10,9,6,5] => [2,3,4,1,6,9,8,10,11,5,12,7] => 00100100101
[(1,6),(2,5),(3,4),(7,8),(9,12),(10,11)] => [6,5,4,3,2,1,8,7,12,11,10,9] => [2,3,4,5,6,1,8,7,10,11,12,9] => 00001010001
[(1,12),(2,11),(3,10),(4,7),(5,6),(8,9)] => [12,11,10,7,6,5,4,9,8,3,2,1] => [2,3,8,5,6,7,9,10,1,11,12,4] => 00100001001
[(1,2),(3,10),(4,7),(5,6),(8,9),(11,12)] => [2,1,10,7,6,5,4,9,8,3,12,11] => [2,1,8,5,6,7,9,10,3,4,12,11] => 10100001001
[(1,2),(3,4),(5,6),(7,10),(8,9),(11,12)] => [2,1,4,3,6,5,10,9,8,7,12,11] => [2,1,4,3,6,5,8,9,10,7,12,11] => 10101000101
[(1,12),(2,3),(4,11),(5,6),(7,10),(8,9)] => [12,3,2,11,6,5,10,9,8,7,4,1] => [4,3,7,8,6,9,10,12,11,5,1,2] => 10010001110
[(1,2),(3,12),(4,11),(5,6),(7,10),(8,9)] => [2,1,12,11,6,5,10,9,8,7,4,3] => [2,1,4,7,6,8,9,10,11,3,12,5] => 10010000101
[(1,4),(2,3),(5,6),(7,10),(8,9),(11,12)] => [4,3,2,1,6,5,10,9,8,7,12,11] => [2,3,4,1,6,5,8,9,10,7,12,11] => 00101000101
[(1,2),(3,4),(5,6),(7,12),(8,9),(10,11)] => [2,1,4,3,6,5,12,9,8,11,10,7] => [2,1,4,3,6,5,10,9,11,12,7,8] => 10101010010
[(1,4),(2,3),(5,6),(7,12),(8,9),(10,11)] => [4,3,2,1,6,5,12,9,8,11,10,7] => [2,3,4,1,6,5,10,9,11,12,7,8] => 00101010010
[(1,12),(2,11),(3,8),(4,7),(5,6),(9,10)] => [12,11,8,7,6,5,4,3,10,9,2,1] => [2,9,4,5,6,7,8,10,11,1,12,3] => 01000000101
[(1,2),(3,8),(4,7),(5,6),(9,10),(11,12)] => [2,1,8,7,6,5,4,3,10,9,12,11] => [2,1,4,5,6,7,8,3,10,9,12,11] => 10000010101
[(1,2),(3,12),(4,7),(5,6),(8,11),(9,10)] => [2,1,12,7,6,5,4,11,10,9,8,3] => [2,1,8,5,6,7,9,10,11,12,3,4] => 10100000010
[(1,8),(2,3),(4,7),(5,6),(9,10),(11,12)] => [8,3,2,7,6,5,4,1,10,9,12,11] => [4,3,5,6,7,8,1,2,10,9,12,11] => 10000100101
[(1,12),(2,9),(3,8),(4,7),(5,6),(10,11)] => [12,9,8,7,6,5,4,3,2,11,10,1] => [10,3,4,5,6,7,8,9,11,12,1,2] => 10000000010
[(1,2),(3,8),(4,7),(5,6),(9,12),(10,11)] => [2,1,8,7,6,5,4,3,12,11,10,9] => [2,1,4,5,6,7,8,3,10,11,12,9] => 10000010001
[(1,10),(2,9),(3,8),(4,7),(5,6),(11,12)] => [10,9,8,7,6,5,4,3,2,1,12,11] => [2,3,4,5,6,7,8,9,10,1,12,11] => 00000000101
[(1,8),(2,3),(4,7),(5,6),(9,12),(10,11)] => [8,3,2,7,6,5,4,1,12,11,10,9] => [4,3,5,6,7,8,1,2,10,11,12,9] => 10000100001
[(1,2),(3,4),(5,6),(7,12),(8,11),(9,10)] => [2,1,4,3,6,5,12,11,10,9,8,7] => [2,1,4,3,6,5,8,9,10,11,12,7] => 10101000001
[(1,8),(2,7),(3,4),(5,6),(9,10),(11,12)] => [8,7,4,3,6,5,2,1,10,9,12,11] => [2,5,4,6,7,1,8,3,10,9,12,11] => 01001010101
[(1,4),(2,3),(5,6),(7,12),(8,11),(9,10)] => [4,3,2,1,6,5,12,11,10,9,8,7] => [2,3,4,1,6,5,8,9,10,11,12,7] => 00101000001
[(1,8),(2,7),(3,4),(5,6),(9,12),(10,11)] => [8,7,4,3,6,5,2,1,12,11,10,9] => [2,5,4,6,7,1,8,3,10,11,12,9] => 01001010001
[(1,12),(2,11),(3,6),(4,5),(7,10),(8,9)] => [12,11,6,5,4,3,10,9,8,7,2,1] => [2,7,4,5,6,8,9,10,11,1,12,3] => 01000000101
[(1,2),(3,6),(4,5),(7,10),(8,9),(11,12)] => [2,1,6,5,4,3,10,9,8,7,12,11] => [2,1,4,5,6,3,8,9,10,7,12,11] => 10001000101
[(1,2),(3,12),(4,5),(6,11),(7,10),(8,9)] => [2,1,12,5,4,11,10,9,8,7,6,3] => [2,1,6,5,7,8,9,10,11,12,3,4] => 10100000010
[(1,6),(2,3),(4,5),(7,10),(8,9),(11,12)] => [6,3,2,5,4,1,10,9,8,7,12,11] => [4,3,5,6,1,2,8,9,10,7,12,11] => 10010000101
[(1,2),(3,6),(4,5),(7,12),(8,9),(10,11)] => [2,1,6,5,4,3,12,9,8,11,10,7] => [2,1,4,5,6,3,10,9,11,12,7,8] => 10001010010
[(1,10),(2,7),(3,6),(4,5),(8,9),(11,12)] => [10,7,6,5,4,3,2,9,8,1,12,11] => [8,3,4,5,6,7,9,10,1,2,12,11] => 10000001001
[(1,6),(2,3),(4,5),(7,12),(8,9),(10,11)] => [6,3,2,5,4,1,12,9,8,11,10,7] => [4,3,5,6,1,2,10,9,11,12,7,8] => 10010010010
[(1,12),(2,5),(3,4),(6,11),(7,10),(8,9)] => [12,5,4,3,2,11,10,9,8,7,6,1] => [6,3,4,5,7,8,9,10,11,12,1,2] => 10000000010
[(1,2),(3,4),(5,12),(6,11),(7,10),(8,9)] => [2,1,4,3,12,11,10,9,8,7,6,5] => [2,1,4,3,6,7,8,9,10,11,12,5] => 10100000001
[(1,6),(2,5),(3,4),(7,10),(8,9),(11,12)] => [6,5,4,3,2,1,10,9,8,7,12,11] => [2,3,4,5,6,1,8,9,10,7,12,11] => 00001000101
[(1,4),(2,3),(5,12),(6,11),(7,10),(8,9)] => [4,3,2,1,12,11,10,9,8,7,6,5] => [2,3,4,1,6,7,8,9,10,11,12,5] => 00100000001
[(1,6),(2,5),(3,4),(7,12),(8,9),(10,11)] => [6,5,4,3,2,1,12,9,8,11,10,7] => [2,3,4,5,6,1,10,9,11,12,7,8] => 00001010010
[(1,12),(2,7),(3,6),(4,5),(8,11),(9,10)] => [12,7,6,5,4,3,2,11,10,9,8,1] => [8,3,4,5,6,7,9,10,11,12,1,2] => 10000000010
[(1,2),(3,6),(4,5),(7,12),(8,11),(9,10)] => [2,1,6,5,4,3,12,11,10,9,8,7] => [2,1,4,5,6,3,8,9,10,11,12,7] => 10001000001
[(1,8),(2,7),(3,6),(4,5),(9,10),(11,12)] => [8,7,6,5,4,3,2,1,10,9,12,11] => [2,3,4,5,6,7,8,1,10,9,12,11] => 00000010101
[(1,6),(2,3),(4,5),(7,12),(8,11),(9,10)] => [6,3,2,5,4,1,12,11,10,9,8,7] => [4,3,5,6,1,2,8,9,10,11,12,7] => 10010000001
[(1,8),(2,7),(3,6),(4,5),(9,12),(10,11)] => [8,7,6,5,4,3,2,1,12,11,10,9] => [2,3,4,5,6,7,8,1,10,11,12,9] => 00000010001
[(1,6),(2,5),(3,4),(7,12),(8,11),(9,10)] => [6,5,4,3,2,1,12,11,10,9,8,7] => [2,3,4,5,6,1,8,9,10,11,12,7] => 00001000001
[(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] => 10101010101
[(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] => 10101010101
[(1,2),(3,4),(5,6),(7,10),(8,11),(9,12)] => [2,1,4,3,6,5,10,11,12,7,8,9] => [2,1,4,3,6,5,12,7,8,10,11,9] => 10101010001
[(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] => 10101010101
[(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] => 10101010101
[(1,2),(3,4),(5,8),(6,9),(7,10),(11,12)] => [2,1,4,3,8,9,10,5,6,7,12,11] => [2,1,4,3,10,5,6,8,9,7,12,11] => 10101000101
[(1,2),(3,4),(5,9),(6,10),(7,11),(8,12)] => [2,1,4,3,9,10,11,12,5,6,7,8] => [2,1,4,3,12,5,6,7,9,10,11,8] => 10101000001
[(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] => 10101010101
[(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] => 10101010101
[(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] => 10101010101
[(1,2),(3,5),(4,6),(7,10),(8,11),(9,12)] => [2,1,5,6,3,4,10,11,12,7,8,9] => [2,1,6,3,5,4,12,7,8,10,11,9] => 10101010001
[(1,2),(3,6),(4,7),(5,8),(9,10),(11,12)] => [2,1,6,7,8,3,4,5,10,9,12,11] => [2,1,8,3,4,6,7,5,10,9,12,11] => 10100010101
[(1,2),(3,6),(4,7),(5,8),(9,11),(10,12)] => [2,1,6,7,8,3,4,5,11,12,9,10] => [2,1,8,3,4,6,7,5,12,9,11,10] => 10100010101
[(1,2),(3,7),(4,8),(5,9),(6,10),(11,12)] => [2,1,7,8,9,10,3,4,5,6,12,11] => [2,1,10,3,4,5,7,8,9,6,12,11] => 10100000101
[(1,2),(3,8),(4,9),(5,10),(6,11),(7,12)] => [2,1,8,9,10,11,12,3,4,5,6,7] => [2,1,12,3,4,5,6,8,9,10,11,7] => 10100000001
[(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] => 10101010101
[(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] => 10101010101
[(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] => 10101010101
[(1,3),(2,4),(5,6),(7,10),(8,11),(9,12)] => [3,4,1,2,6,5,10,11,12,7,8,9] => [4,1,3,2,6,5,12,7,8,10,11,9] => 10101010001
[(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] => 10101010101
[(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] => 10101010101
[(1,3),(2,4),(5,8),(6,9),(7,10),(11,12)] => [3,4,1,2,8,9,10,5,6,7,12,11] => [4,1,3,2,10,5,6,8,9,7,12,11] => 10101000101
[(1,3),(2,4),(5,9),(6,10),(7,11),(8,12)] => [3,4,1,2,9,10,11,12,5,6,7,8] => [4,1,3,2,12,5,6,7,9,10,11,8] => 10101000001
[(1,4),(2,5),(3,6),(7,8),(9,10),(11,12)] => [4,5,6,1,2,3,8,7,10,9,12,11] => [6,1,2,4,5,3,8,7,10,9,12,11] => 10001010101
[(1,4),(2,5),(3,6),(7,8),(9,11),(10,12)] => [4,5,6,1,2,3,8,7,11,12,9,10] => [6,1,2,4,5,3,8,7,12,9,11,10] => 10001010101
[(1,4),(2,5),(3,6),(7,9),(8,10),(11,12)] => [4,5,6,1,2,3,9,10,7,8,12,11] => [6,1,2,4,5,3,10,7,9,8,12,11] => 10001010101
[(1,4),(2,5),(3,6),(7,10),(8,11),(9,12)] => [4,5,6,1,2,3,10,11,12,7,8,9] => [6,1,2,4,5,3,12,7,8,10,11,9] => 10001010001
[(1,5),(2,6),(3,7),(4,8),(9,10),(11,12)] => [5,6,7,8,1,2,3,4,10,9,12,11] => [8,1,2,3,5,6,7,4,10,9,12,11] => 10000010101
[(1,5),(2,6),(3,7),(4,8),(9,11),(10,12)] => [5,6,7,8,1,2,3,4,11,12,9,10] => [8,1,2,3,5,6,7,4,12,9,11,10] => 10000010101
[(1,6),(2,7),(3,8),(4,9),(5,10),(11,12)] => [6,7,8,9,10,1,2,3,4,5,12,11] => [10,1,2,3,4,6,7,8,9,5,12,11] => 10000000101
[(1,7),(2,8),(3,9),(4,10),(5,11),(6,12)] => [7,8,9,10,11,12,1,2,3,4,5,6] => [12,1,2,3,4,5,7,8,9,10,11,6] => 10000000001
Map
to permutation
Description
Returns the fixed point free involution whose transpositions are the pairs in the perfect matching.
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
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.