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The growth series of compact hyperbolic Coxeter groups with 4 and 5 generators |
Canad. Math. Bull. 41(1998), 231-239
Published:1998-06-01
Printed: Jun 1998
Printed: Jun 1998
- R. L. Worthington
Abstract
The growth series of compact hyperbolic Coxeter groups with 4 and 5
generators are explicitly calculated. The assertions of J.~Cannon
and Ph.~Wagreich for the 4-generated groups, that the poles of the
growth series lie
on the unit circle, with the exception of a single real reciprocal pair of
poles, are verified. We also verify that for the 5-generated groups, this
phenomenon fails.
| MSC Classifications: |
20F05 - Generators, relations, and presentations 20F55 - Reflection and Coxeter groups [See also 22E40, 51F15] |