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2014 The growth function of Coxeter dominoes and $2$–Salem numbers
Yuriko Umemoto
Algebr. Geom. Topol. 14(5): 2721-2746 (2014). DOI: 10.2140/agt.2014.14.2721

Abstract

By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in 2 and 3 is a Salem number. Kerada defined a j–Salem number, which is a generalization of Salem numbers. In this paper, we realize infinitely many 2–Salem numbers as the growth rates of cocompact Coxeter groups in 4. Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes, which we call Coxeter dominoes.

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Yuriko Umemoto. "The growth function of Coxeter dominoes and $2$–Salem numbers." Algebr. Geom. Topol. 14 (5) 2721 - 2746, 2014. https://doi.org/10.2140/agt.2014.14.2721

Information

Received: 20 May 2013; Revised: 4 September 2013; Accepted: 10 September 2013; Published: 2014
First available in Project Euclid: 19 December 2017

zbMATH: 1307.20036
MathSciNet: MR3276846
Digital Object Identifier: 10.2140/agt.2014.14.2721

Subjects:
Primary: 20F55
Secondary: 11K16, 20F65

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.14 • No. 5 • 2014
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