A new geometric approach to Sturmian words

Details A new geometric approach to Sturmian words A new geometric approach to Sturmian words

2012-01-21

arxiv.org/abs/1201.4468v1

Computer Science

Discrete Mathematics

12 pages, 7 figures. A preprint of a paper to appear in Theoretical Computer Science

Scientific paper

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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