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Some combinatorial properties of Sturmian words. (English) Zbl 0874.68245
Summary: We give a characterization of finite Sturmian words, by palindrome words, which generalizes a property of the Fibonacci words. We prove that the set $$St$$ of finite Sturmian words coincides with the set of the factors of all the words $$w$$ such that $$w=AB=Cxy$$ with $$A$$, $$B$$, $$C$$ palindromes, $$x$$, $$y\in {a, b}$$ and $$x\neq y$$. Moreover, using this result we prove that $$St$$ is equal to the set of the factors of all words w having two periods $$p$$ and $$q$$ which are coprimes and such that $$|w|\geq p+q-2$$. Several other combinatorial properties concerning special and bispecial elements of $$St$$ are shown. As a consequence we give a new, and purely combinatorial, proof of the enumeration formula of $$St$$.

##### MSC:
 68R15 Combinatorics on words 05A15 Exact enumeration problems, generating functions
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##### References:
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