English

Rational Gluing in Edge Replacement Systems

Group Theory 2025-03-24 v2 Metric Geometry

Abstract

In this paper, we prove the rationality of the gluing relation of edge replacement systems, which were introduced for studying rearrangement groups of fractals. More precisely, we describe an algorithmic procedure for building a finite state automaton that recognizes pairs of equivalent sequences that are glued in the fractal. This fits in recent interest towards the rationality of gluing relations on totally disconnected compact metrizable spaces.

Keywords

Cite

@article{arxiv.2403.09276,
  title  = {Rational Gluing in Edge Replacement Systems},
  author = {Davide Perego and Matteo Tarocchi},
  journal= {arXiv preprint arXiv:2403.09276},
  year   = {2025}
}

Comments

Final version, section and theorem numbering as published. 14 pages

R2 v1 2026-06-28T15:19:54.257Z