Identifier
Values
[1,0] => 10 => 00 => 01 => 0
[1,0,1,0] => 1010 => 0010 => 0101 => 1
[1,1,0,0] => 1100 => 0100 => 1001 => 1
[1,0,1,0,1,0] => 101010 => 001010 => 010101 => 2
[1,0,1,1,0,0] => 101100 => 001100 => 010011 => 1
[1,1,0,0,1,0] => 110010 => 010010 => 100101 => 2
[1,1,0,1,0,0] => 110100 => 010100 => 101001 => 2
[1,1,1,0,0,0] => 111000 => 011000 => 100011 => 1
[1,0,1,0,1,0,1,0] => 10101010 => 00101010 => 01010101 => 3
[1,0,1,0,1,1,0,0] => 10101100 => 00101100 => 01010011 => 2
[1,0,1,1,0,0,1,0] => 10110010 => 00110010 => 01001101 => 2
[1,0,1,1,0,1,0,0] => 10110100 => 00110100 => 01011001 => 2
[1,0,1,1,1,0,0,0] => 10111000 => 00111000 => 01000111 => 1
[1,1,0,0,1,0,1,0] => 11001010 => 01001010 => 10010101 => 3
[1,1,0,0,1,1,0,0] => 11001100 => 01001100 => 10010011 => 2
[1,1,0,1,0,0,1,0] => 11010010 => 01010010 => 10100101 => 3
[1,1,0,1,0,1,0,0] => 11010100 => 01010100 => 10101001 => 3
[1,1,0,1,1,0,0,0] => 11011000 => 01011000 => 10100011 => 2
[1,1,1,0,0,0,1,0] => 11100010 => 01100010 => 10001101 => 2
[1,1,1,0,0,1,0,0] => 11100100 => 01100100 => 10011001 => 2
[1,1,1,0,1,0,0,0] => 11101000 => 01101000 => 10110001 => 2
[1,1,1,1,0,0,0,0] => 11110000 => 01110000 => 10000111 => 1
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0010101010 => 0101010101 => 4
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0010101100 => 0101010011 => 3
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0010110010 => 0101001101 => 3
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0010110100 => 0101011001 => 3
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0010111000 => 0101000111 => 2
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0011001010 => 0100110101 => 3
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0011001100 => 0100110011 => 2
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0011010010 => 0101100101 => 3
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0011010100 => 0101101001 => 3
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0011100010 => 0100011101 => 2
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0011101000 => 0101110001 => 2
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0011110000 => 0100001111 => 1
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 0100101010 => 1001010101 => 4
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 0100110100 => 1001011001 => 3
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 0101001010 => 1010010101 => 4
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 0101010010 => 1010100101 => 4
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 0101010100 => 1010101001 => 4
[1,1,0,1,1,0,0,1,0,0] => 1101100100 => 0101100100 => 1010011001 => 3
[1,1,0,1,1,0,1,0,0,0] => 1101101000 => 0101101000 => 1010110001 => 3
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0110010010 => 1001100101 => 3
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 0110010100 => 1001101001 => 3
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0110100010 => 1011000101 => 3
[1,1,1,0,1,0,0,1,0,0] => 1110100100 => 0110100100 => 1011001001 => 3
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 0110101000 => 1011010001 => 3
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 0111001000 => 1001110001 => 2
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 0111010000 => 1011100001 => 2
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 001010101010 => 010101010101 => 5
[1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 001010101100 => 010101010011 => 4
[1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 001010110010 => 010101001101 => 4
[1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 001010110100 => 010101011001 => 4
[1,0,1,0,1,0,1,1,1,0,0,0] => 101010111000 => 001010111000 => 010101000111 => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 001011001010 => 010100110101 => 4
[1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 001011001100 => 010100110011 => 3
[1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 001011010010 => 010101100101 => 4
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 001011010100 => 010101101001 => 4
[1,0,1,0,1,1,1,0,0,0,1,0] => 101011100010 => 001011100010 => 010100011101 => 3
[1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 001011101000 => 010101110001 => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => 101011110000 => 001011110000 => 010100001111 => 2
[1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 001100101010 => 010011010101 => 4
[1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 001100101100 => 010011010011 => 3
[1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 001100110010 => 010011001101 => 3
[1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 001100111000 => 010011000111 => 2
[1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 001101001010 => 010110010101 => 4
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 001101010010 => 010110100101 => 4
[1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 001101010100 => 010110101001 => 4
[1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 001101100100 => 010110011001 => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 001101101000 => 010110110001 => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => 101110001010 => 001110001010 => 010001110101 => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => 101110001100 => 001110001100 => 010001110011 => 2
[1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 001110100010 => 010111000101 => 3
[1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 001110100100 => 010111001001 => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 001110101000 => 010111010001 => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => 101111000010 => 001111000010 => 010000111101 => 2
[1,0,1,1,1,1,0,1,0,0,0,0] => 101111010000 => 001111010000 => 010111100001 => 2
[1,0,1,1,1,1,1,0,0,0,0,0] => 101111100000 => 001111100000 => 010000011111 => 1
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 010010101010 => 100101010101 => 5
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 010010110100 => 100101011001 => 4
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 010011010010 => 100101100101 => 4
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 010011010100 => 100101101001 => 4
[1,1,0,0,1,1,1,0,1,0,0,0] => 110011101000 => 010011101000 => 100101110001 => 3
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 010100101010 => 101001010101 => 5
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 010100110100 => 101001011001 => 4
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 010101001010 => 101010010101 => 5
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 010101010010 => 101010100101 => 5
[1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 010101010100 => 101010101001 => 5
[1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 010101100100 => 101010011001 => 4
[1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 010101101000 => 101010110001 => 4
[1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 010110010010 => 101001100101 => 4
[1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 010110010100 => 101001101001 => 4
[1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 010110100010 => 101011000101 => 4
[1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 010110100100 => 101011001001 => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 010110101000 => 101011010001 => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => 110111001000 => 010111001000 => 101001110001 => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => 110111010000 => 010111010000 => 101011100001 => 3
[1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 011001001010 => 100110010101 => 4
[1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 011001010010 => 100110100101 => 4
[1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 011001010100 => 100110101001 => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 011001100100 => 100110011001 => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => 111001101000 => 011001101000 => 100110110001 => 3
>>> Load all 119 entries. <<<
[1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 011010001010 => 101100010101 => 4
[1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 011010010010 => 101100100101 => 4
[1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 011010010100 => 101100101001 => 4
[1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 011010100010 => 101101000101 => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => 111010100100 => 011010100100 => 101101001001 => 4
[1,1,1,0,1,0,1,0,1,0,0,0] => 111010101000 => 011010101000 => 101101010001 => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 011011000100 => 101100011001 => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => 111011001000 => 011011001000 => 101100110001 => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => 111011010000 => 011011010000 => 101101100001 => 3
[1,1,1,1,0,0,1,0,0,0,1,0] => 111100100010 => 011100100010 => 100111000101 => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => 111100100100 => 011100100100 => 100111001001 => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => 111100101000 => 011100101000 => 100111010001 => 3
[1,1,1,1,0,1,0,0,0,0,1,0] => 111101000010 => 011101000010 => 101110000101 => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => 111101000100 => 011101000100 => 101110001001 => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => 111101001000 => 011101001000 => 101110010001 => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => 111101010000 => 011101010000 => 101110100001 => 3
[1,1,1,1,1,0,0,1,0,0,0,0] => 111110010000 => 011110010000 => 100111100001 => 2
[1,1,1,1,1,0,1,0,0,0,0,0] => 111110100000 => 011110100000 => 101111000001 => 2
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Description
The number of descents of a binary word.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
path rowmotion
Description
Return the rowmotion of the binary word, regarded as a lattice path.
Consider the binary word of length $n$ as a lattice path with $n$ steps, where a 1 corresponds to an up step and a 0 corresponds to a down step.
This map returns the path whose peaks are the valleys of the original path with an up step appended.
Map
twist
Description
Return the binary word with first letter inverted.