Interval exchanges, admissibility and branching Rauzy induction
Discrete Mathematics
2015-02-25 v3 Combinatorics
Abstract
We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular interval exchange set is a regular interval exchange set with the same number of intervals. Derivation is taken here with respect to return words. We characterize the admissible intervals using a branching version of the Rauzy induction. We also study the case of regular interval exchange transformations defined over a quadratic field and show that the set of factors of such a transformation is primitive morphic. The proof uses an extension of a result of Boshernitzan and Carroll.
Keywords
Cite
@article{arxiv.1305.0120,
title = {Interval exchanges, admissibility and branching Rauzy induction},
author = {Francesco Dolce and Dominique Perrin},
journal= {arXiv preprint arXiv:1305.0120},
year = {2015}
}