Identifier
Values
[1,0] => 10 => 10 => 1
[1,0,1,0] => 1010 => 1100 => 2
[1,1,0,0] => 1100 => 1010 => 4
[1,0,1,0,1,0] => 101010 => 111000 => 3
[1,0,1,1,0,0] => 101100 => 101100 => 5
[1,1,0,0,1,0] => 110010 => 101100 => 5
[1,1,0,1,0,0] => 110100 => 110010 => 7
[1,1,1,0,0,0] => 111000 => 100110 => 6
[1,0,1,0,1,0,1,0] => 10101010 => 11110000 => 4
[1,0,1,0,1,1,0,0] => 10101100 => 10111000 => 6
[1,0,1,1,0,0,1,0] => 10110010 => 10111000 => 6
[1,0,1,1,0,1,0,0] => 10110100 => 11010100 => 12
[1,0,1,1,1,0,0,0] => 10111000 => 10011010 => 13
[1,1,0,0,1,0,1,0] => 11001010 => 10111000 => 6
[1,1,0,0,1,1,0,0] => 11001100 => 11001100 => 8
[1,1,0,1,0,0,1,0] => 11010010 => 11010100 => 12
[1,1,0,1,0,1,0,0] => 11010100 => 11100010 => 10
[1,1,0,1,1,0,0,0] => 11011000 => 10101100 => 10
[1,1,1,0,0,0,1,0] => 11100010 => 10011010 => 13
[1,1,1,0,0,1,0,0] => 11100100 => 11001010 => 14
[1,1,1,0,1,0,0,0] => 11101000 => 10100110 => 11
[1,1,1,1,0,0,0,0] => 11110000 => 10001110 => 8
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 1111100000 => 5
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 1011110000 => 7
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 1011110000 => 7
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 1101101000 => 14
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 1011110000 => 7
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 1100111000 => 9
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 1101101000 => 14
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 1110100100 => 16
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 1001111000 => 8
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 1100110010 => 17
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 1010101010 => 25
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 1000110110 => 16
[1,1,0,0,1,0,1,0,1,0] => 1100101010 => 1011110000 => 7
[1,1,0,0,1,0,1,1,0,0] => 1100101100 => 1100111000 => 9
[1,1,0,0,1,1,0,0,1,0] => 1100110010 => 1100111000 => 9
[1,1,0,0,1,1,0,1,0,0] => 1100110100 => 1110001100 => 11
[1,1,0,1,0,0,1,0,1,0] => 1101001010 => 1101101000 => 14
[1,1,0,1,0,0,1,1,0,0] => 1101001100 => 1110001100 => 11
[1,1,0,1,0,1,0,0,1,0] => 1101010010 => 1110100100 => 16
[1,1,0,1,0,1,0,1,0,0] => 1101010100 => 1111000010 => 13
[1,1,0,1,0,1,1,0,0,0] => 1101011000 => 1011011000 => 12
[1,1,0,1,1,0,0,0,1,0] => 1101100010 => 1001111000 => 8
[1,1,0,1,1,0,0,1,0,0] => 1101100100 => 1101010100 => 20
[1,1,0,1,1,0,1,0,0,0] => 1101101000 => 1011001100 => 13
[1,1,0,1,1,1,0,0,0,0] => 1101110000 => 1000111100 => 9
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 1100110010 => 17
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 1110010010 => 18
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 1010101010 => 25
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 1001011010 => 21
[1,1,1,1,0,0,0,0,1,0] => 1111000010 => 1000110110 => 16
[1,1,1,1,0,0,0,1,0,0] => 1111000100 => 1010010110 => 19
[1,1,1,1,0,1,0,0,0,0] => 1111010000 => 1001001110 => 14
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 1000011110 => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => 101010101010 => 111111000000 => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => 101010101100 => 101111100000 => 8
[1,0,1,0,1,0,1,1,0,0,1,0] => 101010110010 => 101111100000 => 8
[1,0,1,0,1,0,1,1,0,1,0,0] => 101010110100 => 110111010000 => 16
[1,0,1,0,1,1,0,0,1,0,1,0] => 101011001010 => 101111100000 => 8
[1,0,1,0,1,1,0,0,1,1,0,0] => 101011001100 => 110101110000 => 14
[1,0,1,0,1,1,0,1,0,0,1,0] => 101011010010 => 110111010000 => 16
[1,0,1,0,1,1,0,1,0,1,0,0] => 101011010100 => 111011001000 => 18
[1,0,1,0,1,1,0,1,1,0,0,0] => 101011011000 => 100111101000 => 17
[1,0,1,0,1,1,1,0,0,1,0,0] => 101011100100 => 110011100010 => 20
[1,0,1,0,1,1,1,0,1,0,0,0] => 101011101000 => 101011010010 => 29
[1,0,1,1,0,0,1,0,1,0,1,0] => 101100101010 => 101111100000 => 8
[1,0,1,1,0,0,1,0,1,1,0,0] => 101100101100 => 110011110000 => 10
[1,0,1,1,0,0,1,1,0,0,1,0] => 101100110010 => 110101110000 => 14
[1,0,1,1,0,0,1,1,0,1,0,0] => 101100110100 => 111010011000 => 17
[1,0,1,1,0,0,1,1,1,0,0,0] => 101100111000 => 101010110100 => 27
[1,0,1,1,0,1,0,0,1,0,1,0] => 101101001010 => 110111010000 => 16
[1,0,1,1,0,1,0,0,1,1,0,0] => 101101001100 => 111001101000 => 19
[1,0,1,1,0,1,0,1,0,0,1,0] => 101101010010 => 111011001000 => 18
[1,0,1,1,0,1,0,1,0,1,0,0] => 101101010100 => 111101000100 => 20
[1,0,1,1,0,1,0,1,1,0,0,0] => 101101011000 => 101011110000 => 12
[1,0,1,1,0,1,1,0,0,0,1,0] => 101101100010 => 100111101000 => 17
[1,0,1,1,0,1,1,0,0,1,0,0] => 101101100100 => 110011101000 => 18
[1,0,1,1,0,1,1,0,1,0,0,0] => 101101101000 => 101011011000 => 19
[1,0,1,1,0,1,1,1,0,0,0,0] => 101101110000 => 100011101100 => 18
[1,0,1,1,1,0,0,1,0,0,1,0] => 101110010010 => 110011100010 => 20
[1,0,1,1,1,0,0,1,0,1,0,0] => 101110010100 => 111001100010 => 21
[1,0,1,1,1,0,1,0,0,0,1,0] => 101110100010 => 101011010010 => 29
[1,0,1,1,1,0,1,0,0,1,0,0] => 101110100100 => 111001001010 => 29
[1,0,1,1,1,0,1,0,1,0,0,0] => 101110101000 => 101101001010 => 31
[1,1,0,0,1,0,1,0,1,0,1,0] => 110010101010 => 101111100000 => 8
[1,1,0,0,1,0,1,0,1,1,0,0] => 110010101100 => 110101110000 => 14
[1,1,0,0,1,0,1,1,0,0,1,0] => 110010110010 => 110011110000 => 10
[1,1,0,0,1,0,1,1,0,1,0,0] => 110010110100 => 111001101000 => 19
[1,1,0,0,1,1,0,0,1,0,1,0] => 110011001010 => 110101110000 => 14
[1,1,0,0,1,1,0,0,1,1,0,0] => 110011001100 => 111000111000 => 12
[1,1,0,0,1,1,0,1,0,0,1,0] => 110011010010 => 111010011000 => 17
[1,1,0,0,1,1,0,1,0,1,0,0] => 110011010100 => 111100010100 => 22
[1,1,0,0,1,1,0,1,1,0,0,0] => 110011011000 => 101100111000 => 14
[1,1,0,0,1,1,1,0,0,0,1,0] => 110011100010 => 101010110100 => 27
[1,1,0,0,1,1,1,0,0,1,0,0] => 110011100100 => 111000101100 => 20
[1,1,0,1,0,0,1,0,1,0,1,0] => 110100101010 => 110111010000 => 16
[1,1,0,1,0,0,1,0,1,1,0,0] => 110100101100 => 111010011000 => 17
[1,1,0,1,0,0,1,1,0,0,1,0] => 110100110010 => 111001101000 => 19
[1,1,0,1,0,0,1,1,0,1,0,0] => 110100110100 => 111100001100 => 14
[1,1,0,1,0,0,1,1,1,0,0,0] => 110100111000 => 101100101100 => 22
>>> Load all 133 entries. <<<
[1,1,0,1,0,1,0,0,1,0,1,0] => 110101001010 => 111011001000 => 18
[1,1,0,1,0,1,0,0,1,1,0,0] => 110101001100 => 111100010100 => 22
[1,1,0,1,0,1,0,1,0,0,1,0] => 110101010010 => 111101000100 => 20
[1,1,0,1,0,1,0,1,0,1,0,0] => 110101010100 => 111110000010 => 16
[1,1,0,1,0,1,0,1,1,0,0,0] => 110101011000 => 101110110000 => 14
[1,1,0,1,0,1,1,0,0,0,1,0] => 110101100010 => 101011110000 => 12
[1,1,0,1,0,1,1,0,0,1,0,0] => 110101100100 => 110110101000 => 23
[1,1,0,1,0,1,1,0,1,0,0,0] => 110101101000 => 101110011000 => 15
[1,1,0,1,0,1,1,1,0,0,0,0] => 110101110000 => 100101110100 => 23
[1,1,0,1,1,0,0,0,1,0,1,0] => 110110001010 => 100111101000 => 17
[1,1,0,1,1,0,0,0,1,1,0,0] => 110110001100 => 101100111000 => 14
[1,1,0,1,1,0,0,1,0,0,1,0] => 110110010010 => 110011101000 => 18
[1,1,0,1,1,0,0,1,0,1,0,0] => 110110010100 => 111010100100 => 25
[1,1,0,1,1,0,0,1,1,0,0,0] => 110110011000 => 110010111000 => 16
[1,1,0,1,1,0,1,0,0,0,1,0] => 110110100010 => 101011011000 => 19
[1,1,0,1,1,0,1,0,0,1,0,0] => 110110100100 => 111010001100 => 18
[1,1,0,1,1,0,1,0,1,0,0,0] => 110110101000 => 101110001100 => 16
[1,1,0,1,1,1,0,0,0,0,1,0] => 110111000010 => 100011101100 => 18
[1,1,1,0,0,0,1,0,1,1,0,0] => 111000101100 => 101010110100 => 27
[1,1,1,0,0,0,1,1,0,1,0,0] => 111000110100 => 101100101100 => 22
[1,1,1,0,0,1,0,0,1,0,1,0] => 111001001010 => 110011100010 => 20
[1,1,1,0,0,1,0,0,1,1,0,0] => 111001001100 => 111000101100 => 20
[1,1,1,0,0,1,0,1,0,0,1,0] => 111001010010 => 111001100010 => 21
[1,1,1,0,0,1,0,1,0,1,0,0] => 111001010100 => 111100100010 => 22
[1,1,1,0,0,1,0,1,1,0,0,0] => 111001011000 => 110010110010 => 26
[1,1,1,0,0,1,1,0,0,1,0,0] => 111001100100 => 111000110010 => 22
[1,1,1,0,1,0,0,0,1,0,1,0] => 111010001010 => 101011010010 => 29
[1,1,1,0,1,0,0,1,0,0,1,0] => 111010010010 => 111001001010 => 29
[1,1,1,0,1,0,0,1,0,1,0,0] => 111010010100 => 111100001010 => 24
[1,1,1,0,1,0,0,1,1,0,0,0] => 111010011000 => 110100101010 => 33
[1,1,1,0,1,0,1,0,0,0,1,0] => 111010100010 => 101101001010 => 31
[1,1,1,0,1,1,0,0,0,1,0,0] => 111011000100 => 101010101010 => 36
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Description
The major index of a binary word.
This is the sum of the positions of descents, i.e., a one followed by a zero.
For words of length $n$ with $a$ zeros, the generating function for the major index is the $q$-binomial coefficient $\binom{n}{a}_q$.
Map
Burrows-Wheeler
Description
The Burrows-Wheeler transform of a binary word.
The Burrows-Wheeler transform of a finite word $w$ is obtained from $w$ by first listing the conjugates of $w$ in lexicographic order and then concatenating the final letters of the conjugates in this order.
Map
to binary word
Description
Return the Dyck word as binary word.