Related papers: On Erd\"os--Szekeres problem and related problems

We survey Kondrat'ev--Landis' conjecture, providing an up-to-date account of the main advances and describing the techniques developed. We complement the overview with references and formulations of the problem in further closely connected…

We introduce the theory of div point sets, which aims to provide a framework to study the combinatoric nature of any set of points in general position on an Euclidean plane. We then show that proving the unsatisfiability of some first-order…

In this paper, we consider saturation problems related to the celebrated Erd\H{o}s--Szekeres convex polygon problem. For each $n \ge 7$, we construct a planar point set of size $(7/8) \cdot 2^{n-2}$ which is saturated for convex $n$-gons.…

We attempt to survey recent results and open problems connected to Lieb-Thirring inequalities.

The ideas here are a continuation of a previous article. Some of the applications of the main ideas in the previous article are explained, along with some limitations of the general ideas. There are situations where additional hypotheses…

This article proposes a unified analytical approach leading to a partial resolution of the Erdos-Straus, Sierpinski conjectures, and their generalization. We introduce an equivalent reformulation of these conjectures while constructing two…

We show an equivalence between a conjecture of Bisztriczky and Fejes T{\'o}th about arrangements of planar convex bodies and a conjecture of Goodman and Pollack about point sets in topological affine planes. As a corollary of this…

We provide new sufficient conditions under which Ryser's conjecture holds.

This note is a continuation of an earlier paper by the authors. We describe improved constructions addressing a question of Erd\H{o}s and Szemer\'edi on sums and products of real numbers along the edges of a graph. We also add a few…

We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.

We derive asymptotic estimates for distribution functions related to the Schinzel-Szekeres function. These results are then used in three different applications: the longest simple path in the divisor graph, a problem of Erd\H{o}s about a…

In this paper, we will continue the investigation of Waring's problem, and give further improvements.

An technically interesting proof of a known theorem.

This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.

We obtain some new inequalities of Chebyshev Type.

We give a survey of current research on G\"{o}del's incompleteness theorems from the following three aspects: classifications of different proofs of G\"{o}del's incompleteness theorems, the limit of the applicability of G\"{o}del's first…

We give a short proof for the Hartogs's extension theorem on (n-1)-complete complex spaces.

We give a more detailed description of the new system of Pl\"ucker-like equations from [4], discuss how it relates to the usual Pl\"ucker equations, and correct a mistake in that article.

A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)

We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…