Related papers: Coupling Dimers to CDT
We review a recently obtained analytical solution of a restricted so-called hard dimers model coupled to two-dimensional CDT. The combinatorial solution is obtained via bijections of causal triangulations with dimers and decorated trees. We…
We review some recent results by Ambjorn et al. (1202.4435) and the authors (1202.4322,1203.5034) in which multicritical points of the CDT matrix model were found and in a particular example identified with a hard dimer model. This…
We consider a model of restricted dimers coupled to two-dimensional causal dynamical triangulations (CDT), where the dimer configurations are restricted in the sense that they do not include dimers in regions of high curvature. It is shown…
Causal dynamical triangulations allows for a non perturbative approach to quantum gravity. In this article a solution for dimers coupled to CDT is presented and some of the conceptual problems that arise are reflected upon.
We propose a duality between quiver gauge theories and the combinatorics of dimer models. The connection is via toric diagrams together with multiplicities associated to points in the diagram (which count multiplicities of fields in the…
We survey some uses of adjoint functors in graph theory pertaining to colourings, complexity reductions, multiplicativity, circular colourings and tree duality. The exposition of these applications through adjoint functors unifies the…
The observed output of an interferometer is the result of interference among the parts of the input light beam traveling along each possible optical path. In complex systems, writing down all these possible optical paths and computing their…
We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. Some results about the visualization of…
We study a model of colored multiwebs, which generalizes the dimer model to allow each vertex to be adjacent to \(n_v\) edges. These objects can be formulated as a random tiling of a graph with partial dimer covers. We examine the case of a…
We present a top-down approach to calorimeter clustering. An algorithm based on minimal spanning tree theory is described briefly.
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
Strengthening the classical concept of Steiner trees, West and Wu [J. Combin. Theory Ser. B 102 (2012), 186--205] introduced the notion of a $T$-connector in a graph $G$ with a set $T$ of terminals. They conjectured that if the set $T$ is…
The mapper construction is a powerful tool from topological data analysis that is designed for the analysis and visualization of multivariate data. In this paper, we investigate a method for stitching a pair of univariate mappers together…
Dyck tilings are certain tilings in the region surrounded by two Dyck paths. We study bijections and combinatorial objects bijective to Dyck tilings, which include Dyck tiling strip (DTS) and Dyck tiling ribbon (DTR) bijections, increasing…
We consider the dimer problem on a non-bipartite graph $G$, where there are two types of dimers one of which we regard impurities. Results of simulations using Markov chain seem to indicate that impurities are tend to distribute on the…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
The subject of the work are pairs of linearly coupled PT-symmetric dimers. Two different settings are introduced, namely, straight-coupled dimers, where each gain site is linearly coupled to one gain and one loss site, and cross-coupled…
The purpose of this note is to give a succinct summary of some basic properties of T-graphs which arise in the study of the dimer model. We focus in particular on the relation between the dimer model on the heaxgonal lattice with a given…
Given a graph $G$ we consider sequentially placing dimers on it, namely choosing a maximal independent subset of edges, i.e. edges that do not share common vertices. We study the number of vertices that do not belong to any edge found in…
Generalizing results of Temperley, Brooks, Smith, Stone and Tutte and others we describe a natural equivalence between three planar objects: weighted bipartite planar graphs; planar Markov chains; and tilings with convex polygons. This…