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