Related papers: Exploring Progressions: A Collection of Problems
Deep learning techniques have become the method of choice for researchers working on algorithmic aspects of recommender systems. With the strongly increased interest in machine learning in general, it has, as a result, become difficult to…
In this paper a small survey is presented on fourteen sequences, such as: G Add-on Sequences, Sieve Sequences, Digital Sequences, Non-Arithmetic Progressions, recreational sequences (Lucky…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
This is a survey of the exciting recent progress made in understanding the complexity of distributed subgraph finding problems. It overviews the results and techniques for assorted variants of subgraph finding problems in various models of…
We continue the work of Eriksen, Freij, and Wastlund [3], who study derangements that descend in blocks of prescribed lengths. We generalize their work to derangements that ascend in some blocks and descend in others. In particular, we…
Curriculum learning--ordering training examples in a sequence to aid machine learning--takes inspiration from human learning, but has not gained widespread acceptance. Static strategies for scoring item difficulty rely on indirect proxy…
This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…
An arithmetic progression is a sequence of integers in which the difference between any two consecutive elements is the same. We investigate the parameterized complexity of two problems related to arithmetic progressions, called Cover by…
Assembling parts into an object is a combinatorial problem that arises in a variety of contexts in the real world and involves numerous applications in science and engineering. Previous related work tackles limited cases with identical unit…
The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…
We prove that for any partition of a set which contains an infinite arithmetic (respectively geometric) progression into two disjoint subsets, at least one of these subsets contains an infinite number of triplets such that each triplet is…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
In response to Jaffe and Quinn [math.HO/9307227], the author discusses forms of progress in mathematics that are not captured by formal proofs of theorems, especially in his own work in the theory of foliations and geometrization of…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
In this article we describe special type of mathematical problems that may help develop teaching methods that motivate students to explore patterns, formulate conjectures and find solutions without only memorizing formulas and procedures.…
The paper addresses aggregation issues for composite (modular) solutions. A systemic view point is suggested for various aggregation problems. Several solution structures are considered: sets, set morphologies, trees, etc. Mainly, the…
This article presents a source list to support departments in creating more equitable, diverse, and inclusive mathematics classrooms. Included are relevant general-interest books, as well as articles and books presenting research results…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
The study guide (textbook) is part of a set of materials designed to support high-quality practical training in physics. It includes a collection of tasks for organizing both in-class and independent work. The guide serves as a foundation…