Related papers: Combinatorial and Additive Number Theory Problem S…
In 2013, Joerg Arndt recorded that the Fibonacci numbers count integer compositions where the first part is greater than the second, the third part is greater than the fourth, etc. We provide a new combinatorial proof that verifies his…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
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…
Substitutability, interchangeability and related concepts in Constraint Programming were introduced approximately twenty years ago and have given rise to considerable subsequent research. We survey this work, classify, and relate the…
In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers. The second author described periods and sometimes precise form of…
The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation,…
We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on "Arithmetic Topology". Three problem sessions were hosted during the workshop in which participants proposed open questions to the audience and…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem…
Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Universit\`a della Svizzera italiana in the…
This paper presents a data-driven analysis of Quark Matter conferences from 2011 to 2025, investigating trends in geographical representation, research emphasis, and methodological strategies. Using a dataset of over 10,000 presentations,…
Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Summer term 2001, to undergraduate Mathematics and Physics students. It covers a few selected topics from perturbation theory at an introductory…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn…
Those lectures revolve around the following problem: given a system of n real polynomials in n variables, count the number of real roots. The first lecture is a course on Newton iteration and alpha-theory. The second describes an…
We prove some general recursions for the numbers of representations of positive integers as a sum x+y, x in X, y in Y, where X,Y are increasing sequences. In particular, we obtain recursions for the number of the Goldbach, Lemoine-Levy,…