Related papers: Six Constructions of Difference Families
The notion of disjoint weighing matrices is introduced as a generalization of orthogonal designs. A recursive construction along with a computer search lead to some infinite classes of disjoint weighing matrices, which in turn are shown to…
We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…
We investigate a family of one dimensional maps for which the bifurcation diagram looks differently than the usual ones. We describe and exemplify various unique and interesting phenomena arising for this family of maps.
We present a comprehensive survey of constructions of the real numbers (from either the rationals or the integers) in a unified fashion, thus providing an overview of most (if not all) known constructions ranging from the earliest attempts…
The main contribution of this paper is a six-step semi-automatic algorithm that obtains a recursion satisfied by a family of determinants by systematically and iteratively applying Laplace expansion to the underlying matrix family. The…
A description of all subsemigroups of $M_2(\mathbb{C})$ which are given by a countable intersection of constructible sets is given. Furthermore, it is shown that they are intersections of constructible semigroups.
Families of alternating knots (links) and tangles are studied using as building block the conway defined as the twisting of two strands. The regular representation of knots assumes the projection has the minimal number of overpassings, and…
We investigate properties of families $F$ of subsets of a finite set in a situation where subsets are incomparable by the binary inclusion relation and a) for any $A\notin F$, there is such set $A'\in F$ that either $A\subset A'$ or…
In this paper, we construct six families of infinite simple conformal superalgebra of finite growth based on our earlier work on constructing vertex operator superalgebras from graded assocaitive algebras. Three subfamilies of these…
We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomial.
We find new constructions of infinite families of skew Hadamard difference sets in elementary abelian groups under the assumption of the existence of cyclotomic strongly regular graphs. Our construction is based on choosing cyclotomic…
The major challenge in designing a discriminative learning algorithm for predicting structured data is to address the computational issues arising from the exponential size of the output space. Existing algorithms make different assumptions…
Pairwise comparisons between alternatives are a well-established tool to decompose decision problems into smaller and more easily tractable sub-problems. However, due to our limited rationality, the subjective preferences expressed by…
Skew partial difference sets (skew PDSs) are recently-introduced combinatorial objects closely related to partial difference sets (PDSs). To date, only one construction approach for non-trivial skew PDSs is known, using bent partitions:…
The problem of bounding the size of a set system under various intersection restrictions has a central place in extremal combinatorics. We investigate the maximum number of disjoint pairs a set system can have in this setting. In…
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…
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…
We investigate several categories related to transition structures, using a mixture of algebraic and topological methods. We show how two such categories are connected by a contravariant adjunction. This is the most detailed of a family of…
We show a one-to-one correspondence between arrangements of d lines in the projective plane, and lines in P^{d-2}. We apply this correspondence to classify (3,q)-nets over the complex numbers for all q<=6. When q=6, we have twelve possible…
We propose some new method of constructing configurations, which consists in consecutive inscribing copies of one underlying configuration. A uniform characterization of the obtained class and the one introduced in our paper untitled…