Related papers: Six Constructions of Difference Families

We present two families of knots which have straight number higher than crossing number. In the case of the second family, we have computed the straight number explicitly. We also give a general theorem about alternating knots that states…

Let $\mathcal{A}\subseteq{[n]\choose a}$ and $\mathcal{B}\subseteq{[n]\choose b}$ be two families of subsets of $[n]$, we say $\mathcal{A}$ and $\mathcal{B}$ are cross-intersecting if $A\cap B\neq \emptyset$ for all $A\in\mathcal{A}$,…

The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…

In this paper, we construct a family of reductive groups, including all reductive groups up to a given rank. We also construct a similar versal family of quasi-split reductive groups. This result generalizes a former result of N.Avni and…

We consider several classes of complete intersection numerical semigroups, aris- ing from many different contexts like algebraic geometry, commutative algebra, coding theory and factorization theory. In particular, we determine all the…

Let $k\ge d\ge 3$ be fixed. Let $\mathcal{F}$ be a $k$-uniform family on $[n]$. Then $\mathcal{F}$ is $(d,s)$-conditionally intersecting if it does not contain $d$ sets with union of size at most $s$ and empty intersection. Answering a…

The problem of selecting a small, yet high quality subset of patterns from a larger collection of itemsets has recently attracted lot of research. Here we discuss an approach to this problem using the notion of decomposable families of…

We study a construction, which produces surfaces $Y \subset P_3$ with cusps. For example we obtain surfaces of degree six with 18, 24 or 27 three-divisible cusps. For sextic surfaces in a particular family of up to 30 cusps the codes of…

A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group $G$. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over…

Two families $\mathcal{A}$ and $\mathcal{B}$ of sets are said to be cross-intersecting if each member of $\mathcal{A}$ intersects each member of $\mathcal{B}$. For any two integers $n$ and $k$ with $0 \leq k \leq n$, let ${[n] \choose \leq…

Let A be a finite subset of the integers or, more generally, of any abelian group, written additively. The set A has "more sums than differences" if |A+A|>|A-A|. A set with this property is called an MSTD set. This paper gives explicit…

The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…

In Part 1, we describe six projective-type model structures on the category of differential graded modules over a differential graded algebra A over a commutative ring R. When R is a field, the six collapse to three and are well-known, at…

For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic…

We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…

A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…

We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not…

We develop the theory of fractal homeomorphisms generated from pairs of overlapping affine iterated function systems.

We characterize a family of number triangles whose production matrices are closely related to the original number triangle. We study a number of such triangles that are of combinatorial significance. For a specific subfamily, these…

Separating hash families are useful combinatorial structures which are generalizations of many well-studied objects in combinatorics, cryptography and coding theory. In this paper, using tools from graph theory and additive number theory,…