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1996 Growth functions and automatic groups
David B. A. Epstein, Anthony R. Iano-Fletcher, Uri Zwick
Experiment. Math. 5(4): 297-315 (1996).


In this paper we study growth functions of automatic and hyperbolic groups. In addition to standard growth functions, we also want to count the number of finite graphs isomorphic to a given finite graph in the ball of radius $n$ around the identity element in the Cayley graph. This topic was introduced to us by K. Saito [1991]. We report on fast methods to compute the growth function once we know the automatic structure. We prove that for a geodesic automatic structure, the growth function for any fixed finite connected graph is a rational function. For a word-hyperbolic group, we show that one can choose the denominator of the rational function independently of the finite graph.


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David B. A. Epstein. Anthony R. Iano-Fletcher. Uri Zwick. "Growth functions and automatic groups." Experiment. Math. 5 (4) 297 - 315, 1996.


Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 0892.20022
MathSciNet: MR1437220

Primary: 20F32

Rights: Copyright © 1996 A K Peters, Ltd.


Vol.5 • No. 4 • 1996
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