The smallest Mealy automaton of intermediate growth

Details The smallest Mealy automaton of intermediate growth The smallest Mealy automaton of intermediate growth

2004-07-18

arxiv.org/abs/math/0407312v1

J. Algebra 295 (2006), no. 2, 387--414

Mathematics

Group Theory

Scientific paper

10.1016/j.jalgebra.2004.08.040

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 $n \to \infty$.

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