Li Peng ; Bo Tan - Sturmian Sequences and Invertible Substitutions

dmtcs:554 - Discrete Mathematics & Theoretical Computer Science, July 1, 2011, Vol. 13 no. 2 - https://doi.org/10.46298/dmtcs.554
Sturmian Sequences and Invertible Substitutions

Authors: Li Peng ; Bo Tan

It is known that a Sturmian sequence S can be defined as a coding of the orbit of rho (called the intercept of S) under a rotation of irrational angle alpha (called the slope). On the other hand, a fixed point of an invertible substitution is Sturmian. Naturally, there are two interrelated questions: (1) Given an invertible substitution, we know that its fixed point is Sturmian. What is the slope and intercept? (2) Which kind of Sturmian sequences can be fixed by certain non-trivial invertible substitutions? In this paper we give a unified treatment to the two questions. We remark that though the results are known, our proof is very elementary and concise.


Volume: Vol. 13 no. 2
Section: Combinatorics
Published on: July 1, 2011
Submitted on: December 27, 2009
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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