| Título: | Isoperimetric Constants and Self-Avoiding Walks and Polygons on Hyperbolic Coxeter Groups |
| Autores: | Bode, Jason S |
| Fecha: |
2007-04-26 2007-04-26 2007-04-26 |
| Publicador: | |
| Fuente: |
Ver documento |
| Tipo: | Dissertation |
| Tema: |
Isoperimetric Self-Avoiding Walk Self-Avoiding Polygon Hyperbolic Group Coxeter Group Cayley Graph Hyperbolic Graph |
| Descripción: |
We study isoperimetric constants of and self-avoiding walks (SAWs) and self-avoiding
polygons (SAPs) on Cayley graphs of hyperbolic Coxeter groups. These
graphs are tilings of the hyperbolic plane. We calculate the isoperimetric constants
of most rank three hyperbolic Coxeter groups and give an estimate for the remainder.
We prove that for all but a few classes of these groups there are exponentially
fewer k-step SAPs than there are k-step SAWs. We prove that this is also true
of any nontrivial free product. Additionally we show that there are exponentially
more k-step SAWs on a free group F_n (resp. a ?free? Coxeter group T_d) than on
any strict subgroup of F_n (resp. T_d). Kenneth Brown, Laurent Saloff-Coste, David Henderson |
| Idioma: | Inglés |
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