Identifier
Values
[1,0] => [1,1,0,0] => 1100 => 0100 => 2
[1,0,1,0] => [1,1,0,1,0,0] => 110100 => 010100 => 2
[1,1,0,0] => [1,1,1,0,0,0] => 111000 => 011000 => 2
[1,0,1,0,1,0] => [1,1,0,1,0,1,0,0] => 11010100 => 01010100 => 2
[1,0,1,1,0,0] => [1,1,0,1,1,0,0,0] => 11011000 => 01011000 => 3
[1,1,0,0,1,0] => [1,1,1,0,0,1,0,0] => 11100100 => 01100100 => 3
[1,1,0,1,0,0] => [1,1,1,0,1,0,0,0] => 11101000 => 01101000 => 3
[1,1,1,0,0,0] => [1,1,1,1,0,0,0,0] => 11110000 => 01110000 => 2
[] => [1,0] => 10 => 00 => 1
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Description
The length of the shortest palindromic decomposition of a binary word.
A palindromic decomposition (paldec for short) of a word $w=a_1,\dots,a_n$ is any list of factors $p_1,\dots,p_k$ such that $w=p_1\dots p_k$ and each $p_i$ is a palindrome, i.e. coincides with itself read backwards.
Map
to binary word
Description
Return the Dyck word as binary word.
Map
prime Dyck path
Description
Return the Dyck path obtained by adding an initial up and a final down step.
Map
twist
Description
Return the binary word with first letter inverted.