Volume 14, issue 5 (2014)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 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
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