Related papers: Graphs, permutations and topological groups
In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
This is the first installment of a book on combinatorial and geometric group theory from the topological point of view. This is a classical subject. The installment contains Chapters 1, 3 and 4, and there are nine chapters in total: 1.…
Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
The goal of this paper is to describe the connections between Perron-Frobenius theory and vertex maps on graphs. In particular, it is shown how Perron-Frobenius theory gives results about the sets of integers that can arise as periods of…
We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamical systems to our setting, we prove results on…
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
This is an expository article on the theory of formal group laws in homotopy theory, with the goal of leading to the connection with higher-dimensional abelian varieties and automorphic forms. These are roughly based on a talk at the…
We reconstruct a quantum group associated with any Lie algebra together with its representation theory from twisted homologies of generalized configuration spaces of disks. Along the way it brings new combinatorics to the theory, but our…
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
This is an introduction to graph theory, from a geometric and analytic viewpoint. A finite graph $X$ is described by its adjacency matrix $d\in M_N(0,1)$, which can be thought of as being a kind of discrete Laplacian, and we first discuss…
The first group of results of this paper concerns the compressibility of finite subgroups of the Cremona groups. The second concerns the embeddability of other groups in the Cremona groups and, conversely, the Cremona groups in other…
We develop a theory of umkehr maps for twisted generalized homology theories. In this theory, interesting umkehr maps, including generalizations of important classical ones, are induced by cartesian morphisms of a certain category opfibred…
We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.
This is a graduate-level introduction to graph theory, corresponding to a quarter-long course. It covers simple graphs, multigraphs as well as their directed analogues, and more restrictive classes such as tournaments, trees and…
Higher-rank graph generalisations of the Popescu-Poisson transform are constructed, allowing us to develop a dilation theory for higher rank operator tuples. These dilations are joint dilations of the families of operators satisfying…
For a given permutation $\pi_n$ in $S_n$, a random permutation graph is formed by including an edge between two vertices $i$ and $j$ if and only if $(i - j) (\pi_n(i) - \pi_n (j)) < 0$. In this paper, we study various statistics of random…
This paper, following (Dymetman:1998), presents an approach to grammar description and processing based on the geometry of cancellation diagrams, a concept which plays a central role in combinatorial group theory (Lyndon-Schuppe:1977). The…