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Parity Index of Binary Words and Powers of Prime Words

2012
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Electronic Journal of Combinatorics
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Let $f$ be a binary word and let ${\cal F}_d(f)$ be the set of words of length $d$ which do not contain $f$ as a factor (alias words that avoid the pattern $f$). A word is called even/odd if it contains an even/odd number of 1s. The parity index of $f$ (of dimension $d$) is introduced as the difference between the number of even words and the number of odd words in ${\cal F}_d(f)$. A word $f$ is called prime if every nontrivial suffix of $f$ is different from the prefix of $f$ of the same

doi:10.37236/2178
fatcat:ygz2ixqc5bbv7cuelsrzt2avmu