Identifier
Values
[1,0] => 10 => 01 => 00 => 1
[1,0,1,0] => 1010 => 0101 => 0000 => 1
[1,1,0,0] => 1100 => 0110 => 0011 => 2
[1,0,1,0,1,0] => 101010 => 010101 => 000000 => 1
[1,0,1,1,0,0] => 101100 => 010110 => 000011 => 2
[1,1,0,0,1,0] => 110010 => 011001 => 001100 => 2
[1,1,0,1,0,0] => 110100 => 011010 => 001111 => 2
[1,1,1,0,0,0] => 111000 => 011100 => 001001 => 3
[1,0,1,0,1,0,1,0] => 10101010 => 01010101 => 00000000 => 1
[1,0,1,0,1,1,0,0] => 10101100 => 01010110 => 00000011 => 2
[1,0,1,1,0,0,1,0] => 10110010 => 01011001 => 00001100 => 2
[1,0,1,1,0,1,0,0] => 10110100 => 01011010 => 00001111 => 2
[1,0,1,1,1,0,0,0] => 10111000 => 01011100 => 00001001 => 3
[1,1,0,0,1,0,1,0] => 11001010 => 01100101 => 00110000 => 2
[1,1,0,0,1,1,0,0] => 11001100 => 01100110 => 00110011 => 2
[1,1,0,1,0,0,1,0] => 11010010 => 01101001 => 00111100 => 2
[1,1,0,1,0,1,0,0] => 11010100 => 01101010 => 00111111 => 2
[1,1,0,1,1,0,0,0] => 11011000 => 01101100 => 00111001 => 2
[1,1,1,0,0,0,1,0] => 11100010 => 01110001 => 00100100 => 3
[1,1,1,0,0,1,0,0] => 11100100 => 01110010 => 00100111 => 3
[1,1,1,0,1,0,0,0] => 11101000 => 01110100 => 00100001 => 3
[1,1,1,1,0,0,0,0] => 11110000 => 01111000 => 00101101 => 4
[1,0,1,0,1,0,1,0,1,0] => 1010101010 => 0101010101 => 0000000000 => 1
[1,0,1,0,1,0,1,1,0,0] => 1010101100 => 0101010110 => 0000000011 => 2
[1,0,1,0,1,1,0,0,1,0] => 1010110010 => 0101011001 => 0000001100 => 2
[1,0,1,0,1,1,0,1,0,0] => 1010110100 => 0101011010 => 0000001111 => 2
[1,0,1,0,1,1,1,0,0,0] => 1010111000 => 0101011100 => 0000001001 => 3
[1,0,1,1,0,0,1,0,1,0] => 1011001010 => 0101100101 => 0000110000 => 2
[1,0,1,1,0,0,1,1,0,0] => 1011001100 => 0101100110 => 0000110011 => 2
[1,0,1,1,0,1,0,0,1,0] => 1011010010 => 0101101001 => 0000111100 => 2
[1,0,1,1,0,1,0,1,0,0] => 1011010100 => 0101101010 => 0000111111 => 2
[1,0,1,1,0,1,1,0,0,0] => 1011011000 => 0101101100 => 0000111001 => 2
[1,0,1,1,1,0,0,0,1,0] => 1011100010 => 0101110001 => 0000100100 => 3
[1,0,1,1,1,0,0,1,0,0] => 1011100100 => 0101110010 => 0000100111 => 3
[1,0,1,1,1,0,1,0,0,0] => 1011101000 => 0101110100 => 0000100001 => 3
[1,0,1,1,1,1,0,0,0,0] => 1011110000 => 0101111000 => 0000101101 => 4
[1,1,1,0,0,0,1,0,1,0] => 1110001010 => 0111000101 => 0010010000 => 3
[1,1,1,0,0,0,1,1,0,0] => 1110001100 => 0111000110 => 0010010011 => 3
[1,1,1,0,0,1,0,0,1,0] => 1110010010 => 0111001001 => 0010011100 => 3
[1,1,1,0,0,1,0,1,0,0] => 1110010100 => 0111001010 => 0010011111 => 3
[1,1,1,0,0,1,1,0,0,0] => 1110011000 => 0111001100 => 0010011001 => 3
[1,1,1,0,1,0,0,0,1,0] => 1110100010 => 0111010001 => 0010000100 => 3
[1,1,1,0,1,0,0,1,0,0] => 1110100100 => 0111010010 => 0010000111 => 3
[1,1,1,0,1,0,1,0,0,0] => 1110101000 => 0111010100 => 0010000001 => 3
[1,1,1,0,1,1,0,0,0,0] => 1110110000 => 0111011000 => 0010001101 => 3
[1,1,1,1,0,0,1,0,0,0] => 1111001000 => 0111100100 => 0010110001 => 4
[1,1,1,1,1,0,0,0,0,0] => 1111100000 => 0111110000 => 0010100101 => 5
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Description
The length of the longest alternating subword.
This is the length of the longest consecutive subword of the form $010...$ or of the form $101...$.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
rotate back-to-front
Description
The rotation of a binary word, last letter first.
This is the word obtained by moving the last letter to the beginnig.
Map
alternating inverse
Description
Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.