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Matching statistic: St001424
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Mapping
Mp00114: Permutations —connectivity set⟶ Binary words
St001424: Binary words ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,2] => 1 => 0
[2,1] => 0 => 0
[1,2,3] => 11 => 1
[1,3,2] => 10 => 0
[2,1,3] => 01 => 0
[2,3,1] => 00 => 1
[3,1,2] => 00 => 1
[3,2,1] => 00 => 1
[1,2,3,4] => 111 => 1
[1,2,4,3] => 110 => 1
[1,3,2,4] => 101 => 0
[1,3,4,2] => 100 => 1
[1,4,2,3] => 100 => 1
[1,4,3,2] => 100 => 1
[2,1,3,4] => 011 => 1
[2,1,4,3] => 010 => 0
[2,3,1,4] => 001 => 1
[2,3,4,1] => 000 => 1
[2,4,1,3] => 000 => 1
[2,4,3,1] => 000 => 1
[3,1,2,4] => 001 => 1
[3,1,4,2] => 000 => 1
[3,2,1,4] => 001 => 1
[3,2,4,1] => 000 => 1
[3,4,1,2] => 000 => 1
[3,4,2,1] => 000 => 1
[4,1,2,3] => 000 => 1
[4,1,3,2] => 000 => 1
[4,2,1,3] => 000 => 1
[4,2,3,1] => 000 => 1
[4,3,1,2] => 000 => 1
[4,3,2,1] => 000 => 1
[1,2,3,4,5] => 1111 => 2
[1,2,3,5,4] => 1110 => 1
[1,2,4,3,5] => 1101 => 1
[1,2,4,5,3] => 1100 => 2
[1,2,5,3,4] => 1100 => 2
[1,2,5,4,3] => 1100 => 2
[1,3,2,4,5] => 1011 => 1
[1,3,2,5,4] => 1010 => 1
[1,3,4,2,5] => 1001 => 1
[1,3,4,5,2] => 1000 => 1
[1,3,5,2,4] => 1000 => 1
[1,3,5,4,2] => 1000 => 1
[1,4,2,3,5] => 1001 => 1
[1,4,2,5,3] => 1000 => 1
[1,4,3,2,5] => 1001 => 1
[1,4,3,5,2] => 1000 => 1
[1,4,5,2,3] => 1000 => 1
[1,4,5,3,2] => 1000 => 1
Description
The number of distinct squares in a binary word. A factor of a word is a sequence of consecutive letters. This statistic records the number of distinct non-empty words $u$ such that $uu$ is a factor of the word. Note that every word of length at least four contains a square.