An inequality for the number of periods in a word

27 May 2020  ·  Gabric Daniel, Rampersad Narad, Shallit Jeffrey ·

We prove an inequality for the number of periods in a word x in terms of the length of x and its initial critical exponent. Next, we characterize all periods of the length-n prefix of a characteristic Sturmian word in terms of the lazy Ostrowski representation of n, and use this result to show that our inequality is tight for infinitely many words x... We propose two related measures of periodicity for infinite words. Finally, we also consider special cases where x is overlap-free or squarefree. read more

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Discrete Mathematics Formal Languages and Automata Theory Combinatorics

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