Extended branching Rauzy induction
Formal Languages and Automata Theory
2025-12-02 v2 Discrete Mathematics
Dynamical Systems
Abstract
Branching Rauzy induction is a two-sided form of Rauzy induction that acts on regular interval exchange transformations (IETs). We introduce an extended form of branching Rauzy induction that applies to arbitrary standard IETs, including non-minimal ones. The procedure generalizes the branching Rauzy method with two induction steps, merging and splitting, to handle equal-length cuts and invariant components respectively. As an application, we show, via a stepwise morphic argument, that all return words in the language of an arbitrary IET cluster in the Burrows-Wheeler sense.
Cite
@article{arxiv.2511.22588,
title = {Extended branching Rauzy induction},
author = {Francesco Dolce and Christian B. Hughes},
journal= {arXiv preprint arXiv:2511.22588},
year = {2025}
}