Related papers: Graph subshifts
We consider minimal, aperiodic symbolic subshifts and show how to characterize the combinatorial property of bounded powers by means of a metric property. For this purpose we construct a family of graphs which all approximate the subshift…
The notions of symbolic matrix system and $\lambda$-graph system for a subshift are generalizations of symbolic matrix and $\lambda$-graph (= finite symbolic matrix) for a sofic shift respectively ([Doc. Math. 4(1999), 285-340]). M. Nasu…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
Motivated by Ziegler's computability-theoretic characterisation of finite absolute presentability between groups, we prove an analogous theorem in symbolic dynamics. We introduce the notion of one subshift being finitely determined over…
This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results…
Consider a family of graphs having a fixed girth and a large size. We give an optimal lower asymptotic bound on the number of even cycles of any constant length, as the order of the graphs tends to infinity.
We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize…
Any finite group can be encoded as the automorphism group of an unlabeled simple graph. Recently Hartke, Kolb, Nishikawa, and Stolee (2010) demonstrated a construction that allows any ordered pair of finite groups to be represented as the…
Let $\Gamma$ be a connected $G$-vertex-transitive graph, let $v$ be a vertex of $\Gamma$ and let $L=G_v^{\Gamma(v)}$ be the permutation group induced by the action of the vertex-stabiliser $G_v$ on the neighbourhood $\Gamma(v)$. Then…
Periodic-finite-type shifts (PFT's) form a class of sofic shifts that strictly contains the class of shifts of finite type (SFT's). In this paper, we investigate how the notion of "period" inherent in the definition of a PFT causes it to…
We show that one can define and effectively compute Stallings graphs for quasi-convex subgroups of automatic groups (\textit{e.g.} hyperbolic groups or right-angled Artin groups). These Stallings graphs are finite labeled graphs, which are…
In this paper we formulate and prove a combinatorial version of the section conjecture for finite groups acting on finite graphs. We apply this result to the study of rational points and show that finite descent is the only obstruction to…
A graph class is monotone if it is closed under taking subgraphs. It is known that a monotone class defined by finitely many obstructions has bounded treewidth if and only if one of the obstructions is a so-called tripod, that is, a…
The usual way to investigate the statistical properties of finitely generated subgroups of free groups, and of finite presentations of groups, is based on the so-called word-based distribution: subgroups are generated (finite presentations…
The group of automorphisms of a symbolic dynamical system is countable, but often very large. For example, for a mixing subshift of finite type, the automorphism group contains isomorphic copies of the free group on two generators and the…
Path sets are spaces of one-sided infinite symbol sequences associated to pointed graphs (G_v_0), which are edge-labeled directed graphs G with a distinguished vertex v_0. Such sets arise naturally as address labels in geometric fractal…
We consider the class of countable groups possessing an action on a finite product of hyperbolic graphs where every infinite order element acts loxodromically. When the graphs are locally finite, we obtain strong structure theorems for the…
We describe an underlying right angled building structure of any graph product of buildings. We describe the automorphism group of the graph product of buildings. We show that the notion of generalized graph product of a collection of…
We derive representation theorems for exchangeable distributions on finite and infinite graphs using elementary arguments based on geometric and graph-theoretic concepts. Our results elucidate some of the key differences, and their…
Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to…