The smallest Mealy automaton of intermediate growth
Group Theory
2009-11-27 v1 Combinatorics
Abstract
In this paper we study the smallest Mealy automaton of intermediate growth, first considered by the last two authors. We describe the automatic transformation monoid it defines, give a formula for the generating series for its (ball volume) growth function, and give sharp asymptotics for its growth function, namely [ F(n) \sim 2^{5/2} 3^{3/4} \pi^{-2} n^{1/4} \exp{\pi\sqrt{n/6}} ] with the ratios of left- to right-hand side tending to 1 as .
Keywords
Cite
@article{arxiv.math/0407312,
title = {The smallest Mealy automaton of intermediate growth},
author = {Laurent Bartholdi and Illya I. Reznykov and Vitaly I. Sushchansky},
journal= {arXiv preprint arXiv:math/0407312},
year = {2009}
}