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On Rationality of the Cogrowth Series
Author(s):
Dmitri
Kouksov
Journal:
Proc. Amer. Math. Soc.
126
(1998),
2845-2847.
MSC (1991):
Primary 20F05, 20P05, 05C38
MathSciNet review:
1487319
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Abstract:
The cogrowth series of a group  depends on the presentation of the group. We show that the cogrowth series of a non-empty presentation is a rational function not equal to 1 if and only if  is finite. Except for the trivial group, this property is independent of presentation.
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- 2.
- R. I. Grigorchuk Symmetrical random walks on discrete groups. In: Multicomponent Random Systems, ed. by R. L. Dobrushin and Ya. G. Sinai. New York-Basel 1980, 285-325. MR 83k:60016
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- S. P. Humphries Cogrowth of groups and the Dedekind-Frobenius group determinant. Math. Proc. of Camb. Phil. Soc. 121 (1997), 193-217. MR 97i:20037
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- H. Kesten Symmetric random walks on groups Trans. Amer. Math. Soc. 92(1959), 146-156. MR 22:253
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- W. Kuich, A. Salomaa Semirings, automata, languages. Berlin; New York: Springer-Verlag, 1986. MR 87h:68093
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- G. Quenell Combinatorics of free product graphs In: Geometry of the Spectrum. Contemporary Math. 173(1994), 257-281. MR 95k:05089
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Additional Information:
Dmitri
Kouksov
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah 84602
Email:
dmitri@math.byu.edu
DOI:
10.1090/S0002-9939-98-04741-8
PII:
S 0002-9939(98)04741-8
Keywords:
Cogrowth of groups,
rational series
Received by editor(s):
March 13, 1997
Communicated by:
Ronald M. Solomon
Copyright of article:
Copyright
1998,
American Mathematical Society
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