Substitutions for tilings $\{p,q\}$
| dc.creator | Margenstern, Maurice | |
| dc.creator | Skordev, Guentcho | |
| dc.date | 2006-11-09 | |
| dc.date.accessioned | 2026-07-07T07:31:40Z | |
| dc.date.available | 2026-07-07T07:31:40Z | |
| dc.description | In this paper we consider tiling $\{p, q \}$ of the Euclidean space and of the hyperbolic space, and its dual graph $Γ_{q, p}$ from a combinatorial point of view. A substitution $σ_{q, p}$ on an appropriate finite alphabet is constructed. The homogeneity of graph $Γ_{q, p}$ and its generation function are the basic tools for the construction. The tree associated with substitution $σ_{q, p}$ is a spanning tree of graph $Γ_{q, p}$. Let $u_n$ be the number of tiles of tiling $\{p, q \}$ of generation $n$. The characteristic polynomial of the transition matrix of substitution $σ_{q, p}$ is a characteristic polynomial of a linear recurrence. The sequence $(u_n)_{n \geq 0}$ is a solution of this recurrence. The growth of sequence $(u_n)_{n \geq 0}$ is given by the dominant root of the characteristic polynomial. | |
| dc.identifier | https://arxiv.org/abs/cs/0611039 | |
| dc.identifier | http://arxiv.org/abs/cs/0611039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/118838 | |
| dc.subject | Computational Geometry | |
| dc.subject | Discrete Mathematics | |
| dc.subject | F.2.2; G.2 | |
| dc.title | Substitutions for tilings $\{p,q\}$ | |
| dc.type | text |