Related papers: Six Constructions of Difference Families
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…
Starting with a novel definition of divided differences, this essay derives and discusses the basic properties of, and facts about, (univariate) divided differences.
Families of objects appear in several contexts, like algebraic topology, theory of deformations, theoretical physics, etc. An unified coordinate-free algebraic framework for families of geometrical quantities is presented here, which allows…
We describe several families of permutation polynomials obtained using functions with linear translators.
We call a family of sets intersecting, if any two sets in the family intersect. In this paper we investigate intersecting families $\mathcal{F}$ of $k$-element subsets of $[n]:=\{1,\ldots, n\},$ such that every element of $[n]$ lies in the…
We show that a conceptually simple covering technique has surprisingly rich applications to density theorems and conjectures on patterns in sets involving set differences. These applications fall into three categories: (i) analogues of…
A More Sums Than Difference (MSTD) set is a finite set of integers $A$ where the cardinality of its sumset, $A+A$, is greater than the cardinality of its difference set, $A-A$. Since addition is commutative while subtraction isn't, it was…
We construct a Borel maximal eventually different family.
An imprimitive symmetric indecomposable association scheme of rank 5 is said to be Higmanian. A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a symmetric divisible design. We establish conditions which…
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.
In this paper, we propose to enumerate all different configurations belonging to a specific class of fractals: A binary initial tile is selected and a finite recursive tiling process is engaged to produce auto-similar binary patterns. For…
We study deterministic constructions of graphs for which the unique completion of low rank matrices is generically possible regardless of the values of the entries. We relate the completability to the presence of some patterns (particular…
We evaluate four families of determinants of matrices, where the entries are sums or differences of generating functions for paths consisting of up-steps, down-steps and level steps. By specialisation, these determinant evaluations have…
This paper addresses the question whether triple arrays can be constructed from Youden squares developed from difference sets. We prove that if the difference set is abelian, then having $-1$ as multiplier is both a necessary and sufficient…
This article gives an elementary and formal 2-categorical construction of a bicategory of right fractions analogous to anafunctors, starting from a 2-category equipped with a family of covering maps that are fully faithful and co-fully…
This paper discusses the question of how to recognize whether an operad is E_n (ie. equivalent to the little n-cubes operad). A construction is given which produces many new examples of E_n operads. This construction is developed in the…
Discriminative patterns are association patterns that occur with disproportionate frequency in some classes versus others, and have been studied under names such as emerging patterns and contrast sets. Such patterns have demonstrated…
A theory of a derivator version of six-functor-formalisms is developed, using an extension of the notion of fibered multiderivator due to the author. Using the language of (op)fibrations of 2-multicategories this has (like a usual fibered…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Almost difference sets have emerged as a fascinating and important area of research as they can produce functions with optimal nonlinearity, cyclic codes, and binary sequences with optimal autocorrelation. This study aims to investigate the…