Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St000296
(load all 6 compositions to match this statistic)
Mapping
St000296: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1
1 => 1
00 => 2
01 => 0
10 => 0
11 => 2
000 => 3
001 => 0
010 => 3
011 => 0
100 => 0
101 => 3
110 => 0
111 => 3
0000 => 4
0001 => 0
0010 => 1
0011 => 0
0100 => 1
0101 => 0
0110 => 4
0111 => 0
1000 => 0
1001 => 4
1010 => 0
1011 => 1
1100 => 0
1101 => 1
1110 => 0
1111 => 4
00000 => 5
00001 => 0
00010 => 1
00011 => 0
00100 => 5
00101 => 0
00110 => 1
00111 => 0
01000 => 1
01001 => 0
01010 => 5
01011 => 0
01100 => 1
01101 => 0
01110 => 5
01111 => 0
10000 => 0
10001 => 5
10010 => 0
10011 => 1
Description
The length of the symmetric border of a binary word. The symmetric border of a word is the longest word which is a prefix and its reverse is a suffix. The statistic value is equal to the length of the word if and only if the word is [[https://en.wikipedia.org/wiki/Palindrome|palindromic]].