Your data matches 1 statistic following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001524
(load all 6 compositions to match this statistic)
Mapping
St001524: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 0
1 => 0
00 => 1
01 => 0
10 => 0
11 => 1
000 => 1
001 => 0
010 => 1
011 => 0
100 => 0
101 => 1
110 => 0
111 => 1
0000 => 2
0001 => 1
0010 => 1
0011 => 0
0100 => 1
0101 => 0
0110 => 2
0111 => 1
1000 => 1
1001 => 2
1010 => 0
1011 => 1
1100 => 0
1101 => 1
1110 => 1
1111 => 2
00000 => 2
00001 => 1
00010 => 1
00011 => 0
00100 => 2
00101 => 1
00110 => 1
00111 => 0
01000 => 1
01001 => 0
01010 => 2
01011 => 1
01100 => 1
01101 => 0
01110 => 2
01111 => 1
10000 => 1
10001 => 2
10010 => 0
10011 => 1
Description
The degree of symmetry of a binary word. For a binary word $w$ of length $n$, this is the number of positions $i\leq n/2$ such that $w_i = w_{n+1-i}$.