Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 5 (2014), 2721-2746.
The growth function of Coxeter dominoes and $2$–Salem numbers
By the results of Cannon, Wagreich and Parry, it is known that the growth rate of a cocompact Coxeter group in and is a Salem number. Kerada defined a –Salem number, which is a generalization of Salem numbers. In this paper, we realize infinitely many –Salem numbers as the growth rates of cocompact Coxeter groups in . Our Coxeter polytopes are constructed by successive gluing of Coxeter polytopes, which we call Coxeter dominoes.
Algebr. Geom. Topol., Volume 14, Number 5 (2014), 2721-2746.
Received: 20 May 2013
Revised: 4 September 2013
Accepted: 10 September 2013
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
Umemoto, Yuriko. The growth function of Coxeter dominoes and $2$–Salem numbers. Algebr. Geom. Topol. 14 (2014), no. 5, 2721--2746. doi:10.2140/agt.2014.14.2721. https://projecteuclid.org/euclid.agt/1513716001