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

In this paper I present some open problems on Coxeter groups and unimodality, together with the main partial results, and computational evidence, that are known about them.

A detailed and rigorous analysis of G\"odel's proof of his first incompleteness theorem is presented. The purpose of this analysis is two-fold. The first is to reveal what G\"odel actually proved to provide a clear and solid foundation upon…

We establish an embedding from the Hecke algebra associated with the edge contraction of a Coxeter system along an edge to the Hecke algebra associated with the original Coxeter system.

We study a matrix analog of the Erd\H{o}s-Falconer distance problems in vector spaces over finite fields. There arises an interesting analysis of certain quadratic matrix Gauss sums.

This is a survey on Kawaguchi-Silverman conjecture.

The work studies some Difference equations, which are connected with Mejer's function.

We prove an improved form of an expectation of Polya and discuss several related questions

This is an update on, and expansion of, our paper Open problems on $\beta\omega$ in the book Open Problems in Topology.

We present and discuss a number of known results and open problems abelian squares in words on small alphabets.

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

This erratum corrects the proof given in \cite{E1,E2} about the existence of $ 3D $ Skyrmions. This is done by changing the arguments of the proof while remaining in the same framework of concentration-compactness. Note however that the use…

In this paper, we will present a new iterative construction for the auxiliary equation of Waring's problem, which seems a little simpler than the one of so called "smooth numbers" in papers [4] and [8], and give same upper bounds of G(k) as…

Recently, Hong Wang and Joshua Zahl announced a proof of the 3-dimensional Kakeya conjecture. This is a survey article on the proof of Kakeya. We introduce the problem, discuss previous work and some of the difficulties of the problem, and…

The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).

We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

In this paper we obtain minimal support properties of solutions of Schr\"odinger equations. We improve previously known conditions on the potential for which the measure of the support of solutions cannot be too small. We also use these…

We continue our investigation of Erd\H{o}s-Ko-Rado (EKR) sets of flags in spherical buildings. In previous work, we used the theory of buildings and Iwahori-Hecke algebras to obtain upper bounds on their size. As the next step towards the…

Maximal estimates for Schr\"odinger means and convergence almost everywhere of sequences of Schr\"odinger means are studied.

The Erd\H{o}s-Szekeres conjecture states that any set of more than $2^{n-2}$ points in the plane with no three on a line contains the vertices of a convex $n$-gon. Erd\H{o}s, Tuza, and Valtr strengthened the conjecture by stating that any…