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The growth function of Coxeter garlands in \({\mathbb{H}^{4}}\)

Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry volume 53, pages 451–460 (2012)Cite this article

Abstract

The growth function W(t) of a Coxeter group W relative to a Coxeter generating set is always a rational function. We prove by an explicit construction that there are infinitely many cocompact Coxeter groups W in hyperbolic 4-space with the following property. All the roots of the denominator of W(t) are on the unit circle except exactly two pairs of real roots.

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Authors and Affiliations

  1. Département de mathématiques, Université de Fribourg, Chemin du Museé 23, 1700, Fribourg, Switzerland

    Thomas Zehrt

  2. Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051, Basel, Switzerland

    Christine Zehrt-Liebendörfer

Authors
  1. Thomas Zehrt
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  2. Christine Zehrt-Liebendörfer
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Correspondence to Thomas Zehrt.

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partially supported by SNF No. 200020-113199.

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Zehrt, T., Zehrt-Liebendörfer, C. The growth function of Coxeter garlands in \({\mathbb{H}^{4}}\) . Beitr Algebra Geom 53, 451–460 (2012). https://doi.org/10.1007/s13366-011-0073-3

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  • DOI: https://doi.org/10.1007/s13366-011-0073-3

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