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

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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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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Keywords

  • Coxeter group
  • Growth Function
  • Polynomials and location of zeros
  • Hyperbolic polytope

Mathematical Subject Classification (2010)

  • Primary 20F55
  • 26C10
  • 52B11