Coxeter Groups and Asynchronous Cellular Automata
Discrete Mathematics
2010-10-12 v1 Dynamical Systems
Abstract
The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic results in the latter domain may lead to insight about the dynamics in the former, and vice-versa. In this article, we highlight some central themes and common structures, and discuss novel approaches to some open and open-ended problems. We introduce the state automaton of an ACA, and show how the root automaton of a Coxeter group is essentially part of the state automaton of a related ACA.
Keywords
Cite
@article{arxiv.1010.1955,
title = {Coxeter Groups and Asynchronous Cellular Automata},
author = {Matthew Macauley and Henning S. Mortveit},
journal= {arXiv preprint arXiv:1010.1955},
year = {2010}
}
Comments
10 pages, 4 figures