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Matching statistic: St001524
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Mapping
Mp00234: Binary words —valleys-to-peaks⟶ Binary words
St001524: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
0 => 1 => 0
1 => 1 => 0
00 => 01 => 0
01 => 10 => 0
10 => 11 => 1
11 => 11 => 1
000 => 001 => 0
001 => 010 => 1
010 => 101 => 1
011 => 101 => 1
100 => 101 => 1
101 => 110 => 0
110 => 111 => 1
111 => 111 => 1
0000 => 0001 => 1
0001 => 0010 => 1
0010 => 0101 => 0
0011 => 0101 => 0
0100 => 1001 => 2
0101 => 1010 => 0
0110 => 1011 => 1
0111 => 1011 => 1
1000 => 1001 => 2
1001 => 1010 => 0
1010 => 1101 => 1
1011 => 1101 => 1
1100 => 1101 => 1
1101 => 1110 => 1
1110 => 1111 => 2
1111 => 1111 => 2
00000 => 00001 => 1
00001 => 00010 => 1
00010 => 00101 => 1
00011 => 00101 => 1
00100 => 01001 => 0
00101 => 01010 => 2
00110 => 01011 => 1
00111 => 01011 => 1
01000 => 10001 => 2
01001 => 10010 => 0
01010 => 10101 => 2
01011 => 10101 => 2
01100 => 10101 => 2
01101 => 10110 => 0
01110 => 10111 => 1
01111 => 10111 => 1
10000 => 10001 => 2
10001 => 10010 => 0
10010 => 10101 => 2
10011 => 10101 => 2
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 $w_i = w_{n+1-i}$.