Related papers: Extremal problems and the combinatorics of sumsets
This collection of sums and integrals has been harvested from the mathematical and physical literature in unstructured ways. Its main use is backtracking the original sources whenever an integral of the reader's application resembles one of…
We study Ramsey like theorems for infinite trees and similar combinatorial tools. As an application we consider the expansion problem for tree algebras.
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years. One of the main reasons for this growth is the tight…
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
An ordered $r$-matching is an $r$-uniform hypergraph matching equipped with an ordering on its vertices. These objects can be viewed as natural generalisations of $r$-dimensional orders. The theory of ordered 2-matchings is well-developed…
We survey results on the hardness of approximating combinatorial optimization problems.
We describe some combinatorial problems in finite projective planes and indicate how R\'edei's theory of lacunary polynomials can be applied to them.
Recent advances in our understanding of higher derived limits carry multiple implications in the fields of condensed and pyknotic mathematics, as well as for the study of strong homology. These implications are thematically diverse,…
The article contains some important classes of multisets. Combinatorial proofs of problems on the number of m-submultisets and m-permutations of multiset elements are considered and effective algorithms for their calculation are given. In…
Certain new inequalities for the sums of factorials are presented.
We describe recent advances in the study of random analogues of combinatorial theorems.
An MSTD set is a finite set of integers with more sums than differences. It is proved that, for infinitely many positive integers $k$, there are infinitely many affinely inequivalent MSTD sets of cardinality $k$. There are several related…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
We prove new quantitative bounds on the additive structure of sets obeying an $L^3$ 'control' assumption, which arises naturally in several questions within additive combinatorics. This has a number of applications - in particular we…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
New lower bounds involving sum, difference, product, and ratio sets for $A\subset \C$ are given.
We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…
In this paper, we consider a question of sum-keeping about a multiplicative subsemigroup and its generator subsets in a semiring, and develop some elementary (collapse) process of the sum-keeping retraction through subsets until one minimal…