A1 Refereed original research article in a scientific journal
A new geometric approach to Sturmian words
Authors: Matomaki K, Saari K
Publisher: ELSEVIER SCIENCE BV
Publication year: 2012
Journal: Theoretical Computer Science
Journal name in source: THEORETICAL COMPUTER SCIENCE
Journal acronym: THEOR COMPUT SCI
Volume: 432
First page : 77
Last page: 84
Number of pages: 8
ISSN: 0304-3975
DOI: https://doi.org/10.1016/j.tcs.2012.01.040
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. (C) 2012 Elsevier B.V. All rights reserved.
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. (C) 2012 Elsevier B.V. All rights reserved.
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