A new geometric approach to Sturmian words



: Matomaki K, Saari K

Publisher: ELSEVIER SCIENCE BV

: 2012

: Theoretical Computer Science

: THEORETICAL COMPUTER SCIENCE

: THEOR COMPUT SCI

: 432

: 77

: 84

: 8

: 0304-3975

DOI: https://doi.org/10.1016/j.tcs.2012.01.040


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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