Related papers: Algorithmic constructions of relative train track …
We study natural linear representations of self-similar groups over finite fields. In particular, we show that if the group is generated by a finite automaton, then obtained matrices are automatic. This shows a new relation between two…
We construct irreducible unitary representations of a finitely generated free group which are weakly contained in the left regular representation and in which a given linear combination of the generators has an eigenvalue. When the…
A rack of order $n$ is a binary operation $\rack$ on a set $X$ of cardinality $n$, such that right multiplication is an automorphism. More precisely, $(X,\rack)$ is a rack provided that the map $x\mapsto x\rack y$ is a bijection for all…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
This paper exploits adjacencies between the orbits of an ordered set P and a consequence of the classification of finite simple groups to, in many cases, exponentially bound the number of automorphisms. Results clearly identify the…
We construct the first known examples of infinite subgroups of the outer automorphism group of Out(A_Gamma), for certain right-angled Artin groups A_Gamma. This is achieved by introducing a new class of graphs, called focused graphs, whose…
We describe a construction of invariant train tracks with irreducible transition matrix for pseudo-Anosov homeomorphisms. This fills what seems to be a gap in the literature concerning the existence of such train tracks. The construction…
A finite tree $T$ with $|V(T)| \geq 2$ is called {\it automorphism-free} if there is no non-trivial automorphism of $T$. Let $\mathcal{AFT}$ be the poset with the element set of all finite automorphism-free trees (up to graph isomorphism)…
Compact sets in constructive mathematics capture our intuition of what computable subsets of the plane (or any other complete metric space) ought to be. A good representation of compact sets provides an efficient means of creating and…
In this study, we take a systematic look at the unrealised part of public transport networks (PTNs) with functional connections. We consider their complement graphs and study their structure. The complement graph $\bar G$ of an unweighted…
Adept traffic models are critical to both planning and closed-loop simulation for autonomous vehicles (AV), and key design objectives include accuracy, diverse multimodal behaviors, interpretability, and downstream compatibility. Recently,…
We show that the following problems are decidable in a rank 2 free group F_2: does a given finitely generated subgroup H contain primitive elements? and does H meet the orbit of a given word u under the action of G, the group of…
In this paper we look at the automorphisms of the multiplicative group of finite nearfields. We find partial results for the actual automorphism groups. We find counting techniques for the size of all finite nearfields. We then show that…
The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…
For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…
We study the synchronous and asynchronous automatic structures on the fundamental group of a graph of groups in which each edge group is finite. Up to a natural equivalence relation, the set of biautomatic structures on such a graph product…
Sampling-based motion-planning algorithms typically rely on nearest-neighbor (NN) queries when constructing a roadmap. Recent results suggest that in various settings NN queries may be the computational bottleneck of such algorithms.…
Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of…
We define a free product of connected simple graphs that is equivalent to several existing definitions when the graphs are vertex-transitive but differs otherwise. The new definition is designed for the automorphism group of the free…