A Mealy machine with polynomial growth of irrational degree
Group Theory
2009-11-27 v2 Combinatorics
Abstract
We consider a very simple Mealy machine (three states over a two-symbol alphabet), and derive some properties of the semigroup it generates. In particular, this is an infinite, finitely generated semigroup; we show that the growth function of its balls behaves asymptotically like n^2.4401..., where this constant is 1 + log(2)/log((1+sqrt(5))/2); that the semigroup satisfies the identity g^6=g^4; and that its lattice of two-sided ideals is a chain.
Keywords
Cite
@article{arxiv.math/0506203,
title = {A Mealy machine with polynomial growth of irrational degree},
author = {Laurent Bartholdi and Illya I. Reznykov},
journal= {arXiv preprint arXiv:math/0506203},
year = {2009}
}
Comments
20 pages, 1 diagram