Related papers: Divisible design digraphs and association schemes
We resolve two problems of [Cameron, Praeger, and Wormald -- Infinite highly arc transitive digraphs and universal covering digraphs, Combinatorica 1993]. First, we construct a locally finite highly arc-transitive digraph with universal…
Let X be a pseudocyclic association scheme in which all the nontrivial relations are strongly regular graphs with the same eigenvalues. We prove that the principal part of the first eigenmatrix of X is a linear combination of an incidence…
A new family of combined subdivision schemes with one tension parameter is proposed by the interpolatory and approximating subdivision schemes. The displacement vectors between the points of interpolatory and approximating subdivision…
The construction of soft noncommutative schemes via toric geometry in arXiv:2108.05328 [math.AG] (D(15.1), NCS(1)) can be generalized and applied to a commutative scheme with a distinguished atlas of reasonably good affine local coordinate…
Structural node embeddings, vectors capturing local connectivity information for each node in a graph, have many applications in data mining and machine learning, e.g., network alignment and node classification, clustering and anomaly…
Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, we explore a pure algebraic…
Graphs are very important mathematical structures used in many applications, one of which is transportation science. When dealing with transportation networks, one deals not only with the network structure, but also with information related…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Comparability graphs are a popular class of graphs. We introduce as the digraph analogue of comparability graphs the class of comparability digraphs. We show that many concepts such as implication classes and the knotting graph for a…
We look at generalized Delaunay graphs in the constrained setting by introducing line segments which the edges of the graph are not allowed to cross. Given an arbitrary convex shape $C$, a constrained Delaunay graph is constructed by adding…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
The present paper is devoted to the study of dimonoids, algebraic structures with two associative binary operations that satisfy a prescribed system of axioms. We investigate the properties of dual dimonoids. In the class of noncommutative…
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
The study of derivations and their generalizations on non-associative algebras has proven to be fundamental in understanding the internal symmetries and algebraic dynamics of such structures. In this paper, we investigate derivations and…
The assumed causal relationships depicted in a DAG are interpreted using a set of rules called D-separation rules. Although these rules can be implemented automatically using standard software, at least a basic understanding of their…
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…
Architected materials possessing physico-chemical properties adaptable to disparate environmental conditions embody a disruptive new domain of materials science. Fueled by advances in digital design and fabrication, materials shaped into…
The motivation of this paper is to investigate the dual Drazin inverse of adjacency matrices arising from several classes of connected dual-number-weighted digraphs over the dual complex algebra. Explicit formulas for the dual Drazin…
We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems.…
In this work, following the Discrete de Rham (DDR) paradigm, we develop an arbitrary-order discrete divdiv complex on general polyhedral meshes. The construction rests 1) on discrete spaces that are spanned by vectors of polynomials whose…