Identifier
Values
[(1,2)] => [1,0] => 10 => 10 => 0
[(1,2),(3,4)] => [1,0,1,0] => 1010 => 0110 => 1
[(1,3),(2,4)] => [1,1,0,0] => 1100 => 1010 => 1
[(1,4),(2,3)] => [1,1,0,0] => 1100 => 1010 => 1
[(1,2),(3,4),(5,6)] => [1,0,1,0,1,0] => 101010 => 100110 => 1
[(1,3),(2,4),(5,6)] => [1,1,0,0,1,0] => 110010 => 010110 => 2
[(1,4),(2,3),(5,6)] => [1,1,0,0,1,0] => 110010 => 010110 => 2
[(1,5),(2,3),(4,6)] => [1,1,0,1,0,0] => 110100 => 011010 => 2
[(1,6),(2,3),(4,5)] => [1,1,0,1,0,0] => 110100 => 011010 => 2
[(1,6),(2,4),(3,5)] => [1,1,1,0,0,0] => 111000 => 101010 => 2
[(1,5),(2,4),(3,6)] => [1,1,1,0,0,0] => 111000 => 101010 => 2
[(1,4),(2,5),(3,6)] => [1,1,1,0,0,0] => 111000 => 101010 => 2
[(1,3),(2,5),(4,6)] => [1,1,0,1,0,0] => 110100 => 011010 => 2
[(1,2),(3,5),(4,6)] => [1,0,1,1,0,0] => 101100 => 110010 => 1
[(1,2),(3,6),(4,5)] => [1,0,1,1,0,0] => 101100 => 110010 => 1
[(1,3),(2,6),(4,5)] => [1,1,0,1,0,0] => 110100 => 011010 => 2
[(1,4),(2,6),(3,5)] => [1,1,1,0,0,0] => 111000 => 101010 => 2
[(1,5),(2,6),(3,4)] => [1,1,1,0,0,0] => 111000 => 101010 => 2
[(1,6),(2,5),(3,4)] => [1,1,1,0,0,0] => 111000 => 101010 => 2
[(1,2),(3,4),(5,6),(7,8)] => [1,0,1,0,1,0,1,0] => 10101010 => 01100110 => 2
[(1,3),(2,4),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => 11001010 => 00110110 => 2
[(1,4),(2,3),(5,6),(7,8)] => [1,1,0,0,1,0,1,0] => 11001010 => 00110110 => 2
[(1,5),(2,3),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => 11010010 => 10010110 => 2
[(1,6),(2,3),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => 11010010 => 10010110 => 2
[(1,7),(2,3),(4,5),(6,8)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,8),(2,3),(4,5),(6,7)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,8),(2,4),(3,5),(6,7)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,7),(2,4),(3,5),(6,8)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,6),(2,4),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => 11100010 => 01010110 => 3
[(1,5),(2,4),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => 11100010 => 01010110 => 3
[(1,4),(2,5),(3,6),(7,8)] => [1,1,1,0,0,0,1,0] => 11100010 => 01010110 => 3
[(1,3),(2,5),(4,6),(7,8)] => [1,1,0,1,0,0,1,0] => 11010010 => 10010110 => 2
[(1,2),(3,5),(4,6),(7,8)] => [1,0,1,1,0,0,1,0] => 10110010 => 10100110 => 2
[(1,2),(3,6),(4,5),(7,8)] => [1,0,1,1,0,0,1,0] => 10110010 => 10100110 => 2
[(1,3),(2,6),(4,5),(7,8)] => [1,1,0,1,0,0,1,0] => 11010010 => 10010110 => 2
[(1,4),(2,6),(3,5),(7,8)] => [1,1,1,0,0,0,1,0] => 11100010 => 01010110 => 3
[(1,5),(2,6),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => 11100010 => 01010110 => 3
[(1,6),(2,5),(3,4),(7,8)] => [1,1,1,0,0,0,1,0] => 11100010 => 01010110 => 3
[(1,7),(2,5),(3,4),(6,8)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,8),(2,5),(3,4),(6,7)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,8),(2,6),(3,4),(5,7)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,7),(2,6),(3,4),(5,8)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,6),(2,7),(3,4),(5,8)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,5),(2,7),(3,4),(6,8)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,4),(2,7),(3,5),(6,8)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,3),(2,7),(4,5),(6,8)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,2),(3,7),(4,5),(6,8)] => [1,0,1,1,0,1,0,0] => 10110100 => 10110010 => 2
[(1,2),(3,8),(4,5),(6,7)] => [1,0,1,1,0,1,0,0] => 10110100 => 10110010 => 2
[(1,3),(2,8),(4,5),(6,7)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,4),(2,8),(3,5),(6,7)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,5),(2,8),(3,4),(6,7)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,6),(2,8),(3,4),(5,7)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,7),(2,8),(3,4),(5,6)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,8),(2,7),(3,4),(5,6)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,8),(2,7),(3,5),(4,6)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,7),(2,8),(3,5),(4,6)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,6),(2,8),(3,5),(4,7)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,5),(2,8),(3,6),(4,7)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,4),(2,8),(3,6),(5,7)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,3),(2,8),(4,6),(5,7)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,2),(3,8),(4,6),(5,7)] => [1,0,1,1,1,0,0,0] => 10111000 => 11010010 => 2
[(1,2),(3,7),(4,6),(5,8)] => [1,0,1,1,1,0,0,0] => 10111000 => 11010010 => 2
[(1,3),(2,7),(4,6),(5,8)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,4),(2,7),(3,6),(5,8)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,5),(2,7),(3,6),(4,8)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,6),(2,7),(3,5),(4,8)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,7),(2,6),(3,5),(4,8)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,8),(2,6),(3,5),(4,7)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,8),(2,5),(3,6),(4,7)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,7),(2,5),(3,6),(4,8)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,6),(2,5),(3,7),(4,8)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,5),(2,6),(3,7),(4,8)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,4),(2,6),(3,7),(5,8)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,3),(2,6),(4,7),(5,8)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,2),(3,6),(4,7),(5,8)] => [1,0,1,1,1,0,0,0] => 10111000 => 11010010 => 2
[(1,2),(3,5),(4,7),(6,8)] => [1,0,1,1,0,1,0,0] => 10110100 => 10110010 => 2
[(1,3),(2,5),(4,7),(6,8)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,4),(2,5),(3,7),(6,8)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,5),(2,4),(3,7),(6,8)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,6),(2,4),(3,7),(5,8)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,7),(2,4),(3,6),(5,8)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,8),(2,4),(3,6),(5,7)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,8),(2,3),(4,6),(5,7)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,7),(2,3),(4,6),(5,8)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,6),(2,3),(4,7),(5,8)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,5),(2,3),(4,7),(6,8)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,4),(2,3),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => 11001100 => 00111010 => 2
[(1,3),(2,4),(5,7),(6,8)] => [1,1,0,0,1,1,0,0] => 11001100 => 00111010 => 2
[(1,2),(3,4),(5,7),(6,8)] => [1,0,1,0,1,1,0,0] => 10101100 => 01110010 => 2
[(1,2),(3,4),(5,8),(6,7)] => [1,0,1,0,1,1,0,0] => 10101100 => 01110010 => 2
[(1,3),(2,4),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => 11001100 => 00111010 => 2
[(1,4),(2,3),(5,8),(6,7)] => [1,1,0,0,1,1,0,0] => 11001100 => 00111010 => 2
[(1,5),(2,3),(4,8),(6,7)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,6),(2,3),(4,8),(5,7)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,7),(2,3),(4,8),(5,6)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,8),(2,3),(4,7),(5,6)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,8),(2,4),(3,7),(5,6)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,7),(2,4),(3,8),(5,6)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,6),(2,4),(3,8),(5,7)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,5),(2,4),(3,8),(6,7)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
[(1,4),(2,5),(3,8),(6,7)] => [1,1,1,0,0,1,0,0] => 11100100 => 01011010 => 3
>>> Load all 124 entries. <<<
[(1,3),(2,5),(4,8),(6,7)] => [1,1,0,1,0,1,0,0] => 11010100 => 10011010 => 2
[(1,2),(3,5),(4,8),(6,7)] => [1,0,1,1,0,1,0,0] => 10110100 => 10110010 => 2
[(1,2),(3,6),(4,8),(5,7)] => [1,0,1,1,1,0,0,0] => 10111000 => 11010010 => 2
[(1,3),(2,6),(4,8),(5,7)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,4),(2,6),(3,8),(5,7)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,5),(2,6),(3,8),(4,7)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,6),(2,5),(3,8),(4,7)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,7),(2,5),(3,8),(4,6)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,8),(2,5),(3,7),(4,6)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,8),(2,6),(3,7),(4,5)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,7),(2,6),(3,8),(4,5)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,6),(2,7),(3,8),(4,5)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,5),(2,7),(3,8),(4,6)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,4),(2,7),(3,8),(5,6)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,3),(2,7),(4,8),(5,6)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,2),(3,7),(4,8),(5,6)] => [1,0,1,1,1,0,0,0] => 10111000 => 11010010 => 2
[(1,2),(3,8),(4,7),(5,6)] => [1,0,1,1,1,0,0,0] => 10111000 => 11010010 => 2
[(1,3),(2,8),(4,7),(5,6)] => [1,1,0,1,1,0,0,0] => 11011000 => 11001010 => 2
[(1,4),(2,8),(3,7),(5,6)] => [1,1,1,0,1,0,0,0] => 11101000 => 01101010 => 3
[(1,5),(2,8),(3,7),(4,6)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,6),(2,8),(3,7),(4,5)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,7),(2,8),(3,6),(4,5)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
[(1,8),(2,7),(3,6),(4,5)] => [1,1,1,1,0,0,0,0] => 11110000 => 10101010 => 3
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Description
The number of ascents of a binary word.
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00096Foata bijection.
Map
to Dyck path
Description
The Dyck path corresponding to the opener-closer sequence of the perfect matching.
Map
to binary word
Description
Return the Dyck word as binary word.