Geodesic
Growth Rates of 3-dimensional Hyperbolic Coxeter Groups are Perron Numbers
Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 405-422

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In this paper we consider the growth rates of 3-dimensional hyperbolic Coxeter polyhedra with at least one dihedral angle of the form $\frac{\pi }{k}$ for an integer $k\ge 7$ . Combining a classical result by Parry with a previous result of ours, we prove that the growth rates of 3-dimensional hyperbolic Coxeter groups are Perron numbers.
DOI : 10.4153/CMB-2017-052-5
Mots-clés : 20F55, 20F65, Coxeter group, growth function, growth rate, Perron number 
Yukita, Tomoshige. Growth Rates of 3-dimensional Hyperbolic Coxeter Groups are Perron Numbers. Canadian mathematical bulletin, Tome 61 (2018) no. 2, pp. 405-422. doi: 10.4153/CMB-2017-052-5
@article{10_4153_CMB_2017_052_5,
     author = {Yukita, Tomoshige},
     title = {Growth {Rates} of 3-dimensional {Hyperbolic} {Coxeter} {Groups} are {Perron} {Numbers}},
     journal = {Canadian mathematical bulletin},
     pages = {405--422},
     year = {2018},
     volume = {61},
     number = {2},
     doi = {10.4153/CMB-2017-052-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2017-052-5/}
}
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