Related papers: Divisible design digraphs and association schemes
One must add arrows which are forced by transitivity to form the transitive closure of a directed graph. We introduce a construction of a transitive directed graph which is formed by adding vertices instead of arrows and which preserves the…
A graph based matching is used to construct aggregation for algebraic multigrid. Effects of inexact coarse grid solve is analyzed numerically for a highly discontinuous convection diffusion coefficient matrix and problems from Florida…
In this paper, we construct an infinite series of 9-class association schemes from a refinement of the partition of Delsarte-Goethals codes by their Lee weights. The explicit expressions of the dual schemes are determined through direct…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
Association schemes are combinatorial objects that allow us solve problems in several branches of mathematics. They have been used in the study of permutation groups and graphs and also in the design of experiments, coding theory, partition…
This is my dissertation about digraphs ordered by pp-constructability. We study in particular smooth digraphs, i.e., digraphs without sources or sinks, tournaments and semicomplete digraphs, orientations of paths and cycles, digraphs with…
In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a…
Hasse diagrams provide a principled means for visualizing the structure of statistical designs constructed by crossing and nesting of experimental factors. They have long been applied for automated construction of linear models and their…
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and…
First we give an overview of the known supplementary difference sets (SDS) (A_i), i=1..4, with parameters (n;k_i;d), where k_i=|A_i| and each A_i is either symmetric or skew and k_1 + ... + k_4 = n + d. Five new Williamson matrices over the…
As shown in earlier work, skew-adjoint linear differential operators, mapping efforts into flows, give rise to Dirac structures on a bounded spatial domain by a proper definition of boundary variables. In the present paper this is extended…
Euclidean distance matrices (EDM) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices (GDMs) that include EDMs. Each…
In this note, we provide several constructions of Deza Cayley graphs over groups having a generalized dihedral subgroup. These constructions are based on a usage of (relative) difference sets.
Programmable structures are systems whose undeformed geometries and material property distributions are deliberately designed to achieve prescribed deformed configurations under specific loading conditions. Inflatable structures are a…
We introduce a new approach to constructing derived deformation groupoids, by considering them as parameter spaces for strong homotopy bialgebras. This allows them to be constructed for all classical deformation problems, such as…
Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series…
Nonhamiltonian interaction of hamiltonian systems is considered. Dynamical equations are constructed by use of symmetric designs on Lie algebras. The results of analysis of these equations show that some class of symmetric designs on Lie…
The new paradigm of heterostructures based on two-dimensional (2D) atomic crystals has already led to the observation of exciting physical phenomena and creation of novel devices. The possibility of combining layers of different 2D…
We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…
This paper considers two closely related concepts, mixed Steiner system and nonuniform group divisible design (GDD). The distinction between the two concepts is the minimum Hamming distance, which is required for mixed Steiner systems but…