Related papers: Six Constructions of Difference Families
We show that there are five types of planar curves such that arrangements of its translates are combinatorially equivalent to an arrangement of lines. These curves can be used to define norms giving constructions with many unit distances…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
We construct many new cyclic (v;r,s;lambda) difference families with v less than or equal 50. In particular we construct the difference families with parameters (45;18,10;9), (45;22,22;21), (47;21,12;12), (47;19,15;12), (47;22,14;14),…
Hypergraphs have seen widespread application in network and data science communities in recent years. We present a survey of recent work to construct auxiliary structures from hypergraphs -- specifically simplicial, relative, and chain…
We present a variety of new results on finite sets A of integers for which the sumset A+A is larger than the difference set A-A, so-called MSTD (more sums than differences) sets. First we show that there is, up to affine transformation, a…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
The collection of branches (maximal linearly ordered sets of nodes) of the tree ${}^{<\omega}\omega$ (ordered by inclusion) forms an almost disjoint family (of sets of nodes). This family is not maximal -- for example, any level of the tree…
For a family $\mathcal{F}$ of subsets of $\{1,2,\ldots,n\}$, let $\mathcal{D}(\mathcal{F}) = \{F\setminus G: F, G \in \mathcal{F}\}$ be the collection of all (setwise) differences of $\mathcal{F}$. The family $\mathcal{F}$ is called a…
A construction sequence for a graph is a listing of the elements of the graph (the set of vertices and edges) such that each edge follows both its endpoints. The construction number of the graph is the number of such sequences. We determine…
In this article we will describe an algorithm to constructively enumerate non-isomorphic Union closed Sets and Moore sets. We confirm the number of isomorphism classes of Union closed Sets and Moore sets on n<=6 elements presented by other…
Some relations between families of two-character CFTs are explained using a slightly generalised coset construction, and the underlying theories (whose existence was only conjectured based on the modular differential equation) are…
A new family of decagonal quasiperiodic tilings are constructed by the use of generalized point substitution processes, which is a new substitution formalism developed by the author [N. Fujita, Acta Cryst. A 65, 342 (2009)]. These tilings…
We study groups generated by sets of pattern avoiding permutations. In the first part of the paper we prove some general results concerning the structure of such groups. In the second part we carry out a case-by-case analysis of groups…
We introduce six new algebraic invariants for rational difference equations. We use these invariants to perform a reduction of order in each case. This reduction of order allows us to find forbidden sets in each case. These six cases…
We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some…
A rectangulation is a decomposition of a rectangle into finitely many rectangles. Via natural equivalence relations, rectangulations can be seen as combinatorial objects with a rich structure, with links to lattice congruences, flip graphs,…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
We review the basic theory of More Sums Than Differences (MSTD) sets, specifically their existence, simple constructions of infinite families, the proof that a positive percentage of sets under the uniform binomial model are MSTD but not if…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…