Sturm numbers and substitution invariance of 3iet words

Details Sturm numbers and substitution invariance of 3iet words Sturm numbers and substitution invariance of 3iet words

2007-10-31

arxiv.org/abs/0710.5845v1

Mathematics

Combinatorics

13pages

Scientific paper

In this paper, we give a necessary condition for an infinite word defined by a non-degenerate interval exchange on three intervals (3iet word) to be invariant by a substitution: a natural parameter associated to this word must be a Sturm number. We deduce some algebraic consequences from this condition concerning the incidence matrix of the associated substitution. As a by-product of our proof, we give a combinatorial characterization of 3iet words.

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