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.

Source : oai:HAL:hal-00990499v1

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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