Related papers: On Two of Erd\"os's Open Problems
General considerations on the Equivalence conjectures and a review of few mathematical results.
We will present several examples in which ideas from ergodic theory can be useful to study some problems in arithmetic and algebraic geometry.
The two envelopes paradox is discussed. By calculating the conditional probability, we arrive at a conditional expectations which differs from existing results.
We improve constants in the Rademacher-Menchov inequality.
We give a reformulation of the Lehmer conjecture about algebraic integers in terms of a simple counting problem modulo p.
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
These lecture notes give an introduction to the Brauer-Manin obstruction to the existence of rational points, focusing on the interplay between theory and computation.
One presents many Concatenated and Operation Sequences, P-Q Relationships, Digital Sequences, Magic Squares, Prime Conjectures, k-Divisibility and Strong Divisibility Sequences, Geometric Conjectures, Proposed problems.
In this note, convergence of random variables will be revisited. We will give the answers to 5 questions among the 6 open questions introduced in (Convergence rates in the law of large numbers and new kinds of convergence of random…
We revamp the existing theory of Euler class groups and present them in as much generality as possible. We remark on two results of Asok-Fasel and indicate some improvements.
In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
We amalgamate two generalizations of Ramsey's Theorem--Ramsey classes and the Erd\H{o}s-Rado Theorem--into the notion of a combinatorial Erd\H{o}s-Rado class. These classes are closely related to Erd\H{o}s-Rado classes, which are those from…
We provide a survey of past research and a list of open problems regarding central simple algebras and the Brauer group over a field, intended both for experts and for beginners.
These notes present an approach to obtaining the basic operations of addition and multiplication on the natural numbers in terms of elementary results about commutative monoids.
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
We discuss recent progress many problems in random matrix theory of a combinatorial nature, including several breakthroughs that solve long standing famous conjectures.
This paper briefly discusses some questions with analytical and topological aspects, with hopefully some useful references on both sides.
We consider some bases in the Hecke algebra and exhibit certain dualities between them.
This document is a brief summary of progress that has been made on the problems posed in the document "Twenty Open Problems in Enumeration of Matchings" (also available from this server as math.CO/9801060). NOTE: This article has now been…