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arXiv · 1201.4468

A new geometric approach to Sturmian words

Kaisa Matomäki·Kalle Saari
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Abstract

We introduce a new geometric approach to Sturmian words by means of a mapping that associates certain lines in the n x n -grid and sets of finite Sturmian words of length n. Using this mapping, we give new proofs of the formulas enumerating the finite Sturmian words and the palindromic finite Sturmian words of a given length. We also give a new proof for the well-known result that a factor of a Sturmian word has precisely two return words.

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Kaisa Matomäki, Kalle Saari. 2012-01-21. A new geometric approach to Sturmian words. https://arxiv.org/abs/1201.4468

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