Related papers: Coassociativity breaking and oriented graphs
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
We extend the clique-coclique inequality, previously known to hold for graphs in association schemes and vertex-transitive graphs, to graphs in homogeneous coherent configurations and 1-walk regular graphs. We further generalize it to a…
In this paper we develop a structure called Link Algebra, in which we present a Set with two binary operations and an axiom system developed from the study of graph theory and set/antiset theory, sowing main theorems and definitions. Once…
Random walk on changing graphs is considered. For sequences of finite graphs increasing monotonically towards a limiting infinite graph, we establish transition probability upper bounds. It yields sufficient transience criteria for simple…
We investigate unimodular random networks. Our motivations include their characterization via reversibility of an associated random walk and their similarities to unimodular quasi-transitive graphs. We extend various theorems concerning…
We consider two or more simple symmetric walks on some graphs, e.g. the real line, the plane or the two dimensional comb lattice, and investigate the properties of the distance among the walkers.
This is a survey on coarse geometry with an emphasis on coarse homology theories.
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs, and focus on their (twisted) cohomology groups. We…
We introduce the notion of vertex coalgebra, a generalization of vertex operator coalgebras. Next we investigate forms of cocommutativity, coassociativity, skew-symmetry, and an endomorphism, $D^*$, which hold on vertex coalgebras. The…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
In this paper we survey the theory of random walks on buildings and associated groups of Lie type and Kac-Moody groups. We begin with an introduction to the theory of Coxeter systems and buildings, taking a largely combinatorial…
We provide a process on the space of coalescing cadlag stable paths and show convergence in the appropriate topology for coalescing stable random walks on the integer lattice.
In this paper we explore a new method of analysis of associative algebras.
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective resistance in connection graphs by focusing on the duality of…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
This is an introductory level survey of some topics from a new branch of fractal analysis -- the theory of self-similar groups. We discuss recent works on random walks on self-similar groups and their applications to the problem of…
Construction of non-isomorphic cospectral graphs is a nontrivial problem in spectral graph theory specially for large graphs. In this paper, we establish that graph theoretical partial transpose of a graph is a potential tool to create…
Language theory, symbolic dynamics, modelisation of viral insertion into the genetic code of a host cell motivate the introduction of new types of bialgebras whose coalgebra parts are not necessarily coassociative. One of the aim of this…
In this paper we study oriented quantum coalgebras which are structures closely related to oriented quantum algebras. We study the relationship between oriented quantum coalgebras and oriented quantum algebras and the relationship between…
In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that…