Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001524
Mapping
Mp00109: Permutations —descent word⟶ Binary words
Mp00269: Binary words —flag zeros to zeros⟶ Binary words
Mp00136: Binary words —rotate back-to-front⟶ Binary words
St001524: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 0 => 0 => 0 => 0
[2,1] => 1 => 1 => 1 => 0
[1,2,3] => 00 => 01 => 10 => 0
[1,3,2] => 01 => 10 => 01 => 0
[2,1,3] => 10 => 00 => 00 => 1
[2,3,1] => 01 => 10 => 01 => 0
[3,1,2] => 10 => 00 => 00 => 1
[3,2,1] => 11 => 11 => 11 => 1
[1,2,3,4] => 000 => 011 => 101 => 1
[1,2,4,3] => 001 => 101 => 110 => 0
[1,3,2,4] => 010 => 000 => 000 => 1
[1,3,4,2] => 001 => 101 => 110 => 0
[1,4,2,3] => 010 => 000 => 000 => 1
[1,4,3,2] => 011 => 110 => 011 => 0
[2,1,3,4] => 100 => 010 => 001 => 0
[2,1,4,3] => 101 => 100 => 010 => 1
[2,3,1,4] => 010 => 000 => 000 => 1
[2,3,4,1] => 001 => 101 => 110 => 0
[2,4,1,3] => 010 => 000 => 000 => 1
[2,4,3,1] => 011 => 110 => 011 => 0
[3,1,2,4] => 100 => 010 => 001 => 0
[3,1,4,2] => 101 => 100 => 010 => 1
[3,2,1,4] => 110 => 001 => 100 => 0
[3,2,4,1] => 101 => 100 => 010 => 1
[3,4,1,2] => 010 => 000 => 000 => 1
[3,4,2,1] => 011 => 110 => 011 => 0
[4,1,2,3] => 100 => 010 => 001 => 0
[4,1,3,2] => 101 => 100 => 010 => 1
[4,2,1,3] => 110 => 001 => 100 => 0
[4,2,3,1] => 101 => 100 => 010 => 1
[4,3,1,2] => 110 => 001 => 100 => 0
[4,3,2,1] => 111 => 111 => 111 => 1
[1,2,3,4,5] => 0000 => 0111 => 1011 => 1
[1,2,3,5,4] => 0001 => 1011 => 1101 => 1
[1,2,4,3,5] => 0010 => 0001 => 1000 => 1
[1,2,4,5,3] => 0001 => 1011 => 1101 => 1
[1,2,5,3,4] => 0010 => 0001 => 1000 => 1
[1,2,5,4,3] => 0011 => 1101 => 1110 => 1
[1,3,2,4,5] => 0100 => 0100 => 0010 => 1
[1,3,2,5,4] => 0101 => 1000 => 0100 => 1
[1,3,4,2,5] => 0010 => 0001 => 1000 => 1
[1,3,4,5,2] => 0001 => 1011 => 1101 => 1
[1,3,5,2,4] => 0010 => 0001 => 1000 => 1
[1,3,5,4,2] => 0011 => 1101 => 1110 => 1
[1,4,2,3,5] => 0100 => 0100 => 0010 => 1
[1,4,2,5,3] => 0101 => 1000 => 0100 => 1
[1,4,3,2,5] => 0110 => 0010 => 0001 => 1
[1,4,3,5,2] => 0101 => 1000 => 0100 => 1
[1,4,5,2,3] => 0010 => 0001 => 1000 => 1
[1,4,5,3,2] => 0011 => 1101 => 1110 => 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 $w_i = w_{n+1-i}$.