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

In this largely expository paper, we will present a list of En -operads and give complete, and in some cases new, proofs of the equivalences between these operads.

This paper is a complement of our recent works on the semilinear Tricomi equations in [8] and[9].

We obtain some results related to Romanoff's theorem.

In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on previously known…

The paper deals with continuous solutions of a Schilling's problem.

We prove some extensions of Andrews inequality.

The basic theme of this paper is the fact that if $A$ is a finite set of integers, then the sum and product sets cannot both be small. A precise formulation of this fact is Conjecture 1 below due to Erd\H os-Szemer\'edi [E-S]. (see also…

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

The objective of this paper is to report on recent progress on Strichartz estimates for the Schr\"odinger equation and to present the state-of-the-art. These estimates have been obtained in Lebesgue spaces, Sobolev spaces and, recently, in…

We give a quintet of proofs resulting from questions posed by Erd\H{o}s. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums, $K_4$-free $4$-critical graphs with few chords in any…

The Erd\H{o}s-Szekeres Theorem stated in terms of graphs says that any red-blue coloring of the edges of the ordered complete graph $K_{rs+1}$ contains a red copy of the monotone increasing path with $r$ edges or a blue copy of the monotone…

We generalise the Elekes-Szab\'o theorem to arbitrary arity and dimension and characterise the complex algebraic varieties without power saving. The characterisation involves certain algebraic subgroups of commutative algebraic groups…

We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.

In this paper, new inequalities connected with the celebrated Steffensen's integral inequality are proved.

We prove new existence and uniqueness results in full Sobolev spaces for the steady-state Oseen problem in a smooth exterior domain of $\mathbb{R}^n$, $n\ge 2$. These results are then employed, on the one hand, in the study of analogous…

The paper is devoted to a somewhat idiosyncratic account of the theorem of de Bruijn-Erd\"{o}s and Hanani from the combinatorics of finite geometries and its various proofs. Among the proofs discussed are the original proofs by de…

We give a new proof of Chen-Lin result with Li-Zhang method.