Related papers: On forbidden sets
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the primary purpose is to provide an ample supply of problems for…
Partial differential equations (PDEs) are at the heart of many mathematical and scientific advances. While great progress has been made on the theory of PDEs of standard types during the last eight decades, the analysis of nonlinear PDEs of…
We survey the variants of Erd\H{o}s' distinct distances problem and the current best bounds for each of those.
This paper discusses the split feasibility problem with polynomials. The sets are semi-algebraic, defined by polynomial inequalities. They can be either convex or nonconvex, either feasible or infeasible. We give semidefinite relaxations…
We provide further explanation of the significance of a construction in a recent paper of Wolf [Israel J. Math. 179 (2010), 253-278] in the context of the problem of finding large subspaces in sumsets.
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
Enlarging on Parts I, II, and III we write more equations in the desired format of the extended abstract theory of composites. We focus on a multitude of equations involving higher order derivatives. The motivation is that results and…
New exceptional (i.e. non-repeating) prime number multiplets are given and formulated in terms of arithmetic progressions, along with laws governing them. Accompanying repeating prime number multiplets are pointed out. Prime number…
The combinatorial properties of partitions with various restrictions on their hooksets are explored. A connection with numerical semigroups extends current results on simultaneous s/t-cores. Conditions that suffice for a partition to…
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman…
Specification of the strongest possible Bell inequalities for arbitrarily complicated physical scenarios -- any number of observers choosing between any number of observables with any number of possible outcomes -- is currently an open…
Academic challenges comprise effective means for (i) advancing the state of the art, (ii) putting in the spotlight of a scientific community specific topics and problems, as well as (iii) closing the gap for under represented communities in…
We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…
We survey recent developments on the Restriction conjecture.
We give a broad survey of recent results in Enumerative Combinatorics and their complexity aspects.
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
A wide range of applications, most notably in comparative genomics, involve the computation of a shortest sorting sequence of operations for a given permutation, where the set of allowed operations is fixed beforehand. Such sequences are…
This is a survey of old and new problems and results in additive number theory.