Related papers: Divisible design digraphs and association schemes
We classify certain non-symmetric commutative association schemes. As an application, we determine all the primitive weakly distance-regular circulant digraphs.
Distance-increasing maps from binary vectors to permutations, namely DIMs, are useful for the construction of permutation arrays. While a simple mapping algorithm defining DIMs of even length is known, existing DIMs of odd length are either…
The main purpose of this paper is to describe various phenomena and certain constructions arising in the process of studying derived noncommutative schemes. Derived noncommutative schemes are defined as differential graded categories of a…
For a weighted digraph without loops $V$, the arc weights of which can be obtained from an undirected graph with loops ${\sf P}$ according to the rule $v_{ij}=p_{ij}-p_{ii}$, the properties are studied. An effective algorithm for…
Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above…
We construct, for every \(0<k<1\), a bounded globally univalent harmonic mapping \[ f=h+\overline g \colon \D\to\C \] such that \[ |g'(z)|\le k|h'(z)|,\qquad z\in\D, \] while the analytic part \(h\) is unbounded. The construction is based…
Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional…
We present an infinite number of construction schemes involving unitary error bases, Hadamard matrices, quantum Latin squares and controlled families, many of which have not previously been described. Our results rely on biunitary…
The obvious way to construct a GDD (group-divisible design) recursively is to use Wilson's Fundamental Construction for GDDs (WFC). Then a PBD (pairwise balanced design) is often obtained by adding a new point to each group of the GDD.…
Architected materials can achieve enhanced properties compared to their plain counterparts. Specific architecting serves as a powerful design lever to achieve targeted behavior without changing the base material. Thus, the connection…
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…
There is a one-to-one correspondence between the point set of a group divisible design (GDD) with $v_1$ groups of $v_2$ points and the edge set of a complete bipartite graph $K_{v_1,v_2}$. A block of GDD corresponds to a subgraph of…
The aim of this paper is to present a construction of $t$-divisible designs for $t>3$, because such divisible designs seem to be missing in the literature. To this end, tools such as finite projective spaces and their algebraic varieties…
We show how derived categories build bridges across the current mathematical mainstream, linking geometric and algebraic, commutative and noncommutative, local and global banks. Arches in these bridges are pieces of semiorthogonal…
New types of designs called nested space-filling designs have been proposed for conducting multiple computer experiments with different levels of accuracy. In this article, we develop several approaches to constructing such designs. The…
Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and…
Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.
The symplectic graph Sp(2d, q) is the collinearity graph of the symplectic space of dimension 2d over a finite field of order q. A k-regular graph on v vertices is a divisible design graph with parameters (v, k, lambda_1, lambda_2 ,m,n) if…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed.