English

A new geometric approach to Sturmian words

Discrete Mathematics 2012-01-24 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.1201.4468,
  title  = {A new geometric approach to Sturmian words},
  author = {Kaisa Matomäki and Kalle Saari},
  journal= {arXiv preprint arXiv:1201.4468},
  year   = {2012}
}

Comments

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