Algebraic & Geometric Topology Volume 14, issue 5 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

The growth function of Coxeter dominoes and $2$–Salem numbers

Yuriko Umemoto

Algebraic & Geometric Topology 14 (2014) 2721–2746

DOI: 10.2140/agt.2014.14.2721

Bibliography

1	M J Bertin, A Decomps-Guilloux, M Grandet-Hugot, M Pathiaux-Delefosse, J P Schreiber, Pisot and Salem numbers, Birkhäuser (1992) MR1187044
2	J W Cannon, P Wagreich, Growth functions of surface groups, Math. Ann. 293 (1992) 239 MR1166120
3	R Charney, M Davis, Reciprocity of growth functions of Coxeter groups, Geom. Dedicata 39 (1991) 373 MR1123152
4	H S M Coxeter, Discrete groups generated by reflections, Ann. of Math. 35 (1934) 588 MR1503182
5	E Ghate, E Hironaka, The arithmetic and geometry of Salem numbers, Bull. Amer. Math. Soc. 38 (2001) 293 MR1824892
6	J E Humphreys, Reflection groups and Coxeter groups, Cambridge Studies Adv. Math. 29, Cambridge Univ. Press (1990) MR1066460
7	R Kellerhals, G Perren, On the growth of cocompact hyperbolic Coxeter groups, European J. Combin. 32 (2011) 1299 MR2838016
8	A J Kempner, On the complex roots of algebraic equations, Bull. Amer. Math. Soc. 41 (1935) 809 MR1563200
9	M Kerada, Une caractérisation de certaines classes d'entiers algébriques généralisant les nombres de Salem, Acta Arith. 72 (1995) 55 MR1346805
10	F Lannér, On complexes with transitive groups of automorphisms, Comm. Sém., Math. Univ. Lund 11 (1950) 71 MR0042129
11	D H Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. 34 (1933) 461 MR1503118
12	F Luo, On a problem of Fenchel, Geom. Dedicata 64 (1997) 277 MR1440561
13	V S Makarov, The Fedorov groups of four-dimensional and five-dimensional Lobačevskiĭspace, from: "Studies in general algebra" (editor V D Belousov), Kišinev. Gos. Univ., Kishinev (1968) 120 MR0259735
14	M R Murty, Prime numbers and irreducible polynomials, Amer. Math. Monthly 109 (2002) 452 MR1901498
15	W Parry, Growth series of Coxeter groups and Salem numbers, J. Algebra 154 (1993) 406 MR1206129
16	J G Ratcliffe, Foundations of hyperbolic manifolds, Graduate Texts in Mathematics 149, Springer (1994) MR1299730
17	P A Samet, Algebraic integers with two conjugates outside the unit circle, Proc. Cambridge Philos. Soc. 49 (1953) 421 MR0056030
18	I Satake, Linear algebra, Pure and Applied Mathematics 29, Marcel Dekker (1975) MR0401789
19	L Schlettwein, Hyperbolische simplexe, Diplomarbeit, Universität Basel (1995)
20	J P Serre, Cohomologie des groupes discrets, from: "Prospects in mathematics", Ann. of Math. Studies 70, Princeton Univ. Press (1971) 77 MR0385006
21	L Solomon, The orders of the finite Chevalley groups, J. Algebra 3 (1966) 376 MR0199275
22	R Steinberg, Endomorphisms of linear algebraic groups, Memoirs of the AMS 80, Amer. Math. Soc. (1968) 108 MR0230728
23	È B Vinberg, Hyperbolic groups of reflections, Uspekhi Mat. Nauk 40 (1985) 29, 255 MR783604
24	R L Worthington, The growth series of compact hyperbolic Coxeter groups with $4$ and $5$ generators, Canad. Math. Bull. 41 (1998) 231 MR1624278
25	T Zehrt, C Zehrt-Liebendörfer, The growth function of Coxeter garlands in $\mathbb{H}^4$, Beitr. Algebra Geom. 53 (2012) 451 MR2971753