Identifier
Values
[1,0] => 10 => 01 => 10 => 0
[1,0,1,0] => 1010 => 0011 => 1001 => 0
[1,1,0,0] => 1100 => 0011 => 1001 => 0
[1,0,1,0,1,0] => 101010 => 001011 => 100101 => 0
[1,0,1,1,0,0] => 101100 => 000111 => 100011 => 2
[1,1,0,0,1,0] => 110010 => 000111 => 100011 => 2
[1,1,0,1,0,0] => 110100 => 000111 => 100011 => 2
[1,1,1,0,0,0] => 111000 => 000111 => 100011 => 2
[1,0,1,0,1,0,1,0] => 10101010 => 00101011 => 10010101 => 0
[1,0,1,0,1,1,0,0] => 10101100 => 00010111 => 10001011 => 2
[1,0,1,1,0,0,1,0] => 10110010 => 00010111 => 10001011 => 2
[1,0,1,1,0,1,0,0] => 10110100 => 00010111 => 10001011 => 2
[1,0,1,1,1,0,0,0] => 10111000 => 00001111 => 10000111 => 0
[1,1,0,0,1,0,1,0] => 11001010 => 00010111 => 10001011 => 2
[1,1,0,0,1,1,0,0] => 11001100 => 00001111 => 10000111 => 0
[1,1,0,1,0,0,1,0] => 11010010 => 00010111 => 10001011 => 2
[1,1,0,1,0,1,0,0] => 11010100 => 00010111 => 10001011 => 2
[1,1,0,1,1,0,0,0] => 11011000 => 00001111 => 10000111 => 0
[1,1,1,0,0,0,1,0] => 11100010 => 00001111 => 10000111 => 0
[1,1,1,0,0,1,0,0] => 11100100 => 00001111 => 10000111 => 0
[1,1,1,0,1,0,0,0] => 11101000 => 00001111 => 10000111 => 0
[1,1,1,1,0,0,0,0] => 11110000 => 00001111 => 10000111 => 0
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Description
Half the length of the longest odd length palindromic prefix of a binary word.
More precisely, this statistic is the largest number $k$ such that the word has a palindromic prefix of length $2k+1$.
Map
runsort
Description
The word obtained by sorting the weakly increasing runs lexicographically.
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
to binary word
Description
Return the Dyck word as binary word.