This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.
Автор: Cameron Peter J Название: Notes on Counting: An Introduction to Enumerative Combinator ISBN: 1108404952 ISBN-13(EAN): 9781108404952 Издательство: Cambridge Academ Рейтинг: Цена: 5702.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, drawn from many years of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study.
Автор: Feng Yuefeng Название: Combinatorial Extremization ISBN: 9814723169 ISBN-13(EAN): 9789814723169 Издательство: World Scientific Publishing Рейтинг: Цена: 3326.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In China, lots of excellent students who are good at maths takes an active part in various maths contests and the best six senior high school students will be selected to form the IMO National Team to compete in the International Mathematical Olympiad.
Combinational optimization (CO) is a topic in applied mathematics, decision science and computer science that consists of finding the best solution from a non-exhaustive search. CO is related to disciplines such as computational complexity theory and algorithm theory, and has important applications in fields such as operations research/management science, artificial intelligence, machine learning, and software engineering.
Advances in Combinatorial Optimization presents a generalized framework for formulating hard combinatorial optimization problems (COPs) as polynomial sized linear programs. Though developed based on the 'traveling salesman problem' (TSP), the framework allows for the formulating of many of the well-known NP-Complete COPs directly (without the need to reduce them to other COPs) as linear programs, and demonstrates the same for three other problems (e.g. the 'vertex coloring problem' (VCP)). This work also represents a proof of the equality of the complexity classes "P" (polynomial time) and "NP" (nondeterministic polynomial time), and makes a contribution to the theory and application of 'extended formulations' (EFs).
On a whole, Advances in Combinatorial Optimization offers new modeling and solution perspectives which will be useful to professionals, graduate students and researchers who are either involved in routing, scheduling and sequencing decision-making in particular, or in dealing with the theory of computing in general.
Описание: This volume contains selected refereed papers based on lectures presented at the "Integers Conference 2011", an international conference in combinatorial number theory that was held in Carrollton, Georgia, United States in October 2011. This was the fifth Integers Conference, held bi-annually since 2003. It featured plenary lectures presented by Ken Ono, Carla Savage, Laszlo Szekely, Frank Thorne, and Julia Wolf, along with sixty other research talks. This volume consists of ten refereed articles, which are expanded and revised versions of talks presented at the conference. They represent a broad range of topics in the areas of number theory and combinatorics including multiplicative number theory, additive number theory, game theory, Ramsey theory, enumerative combinatorics, elementary number theory, the theory of partitions, and integer sequences.
Автор: Le Roux Название: Combinatorial Inference In Geometri ISBN: 1498781616 ISBN-13(EAN): 9781498781619 Издательство: Taylor&Francis Рейтинг: Цена: 16843.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Combinatorial Inference in Geometric Data Analysis gives an overview of multidimensional statistical inference methods applicable to clouds of points that make no assumption on the process of generating data or distributions, and that are not based on random modelling but on permutation procedures recasting in a combinatorial framework.
Автор: Kyriakos Kalorkoti, Leonid Bokut, Pavel Kolesnikov, Viktor E Lopatkin, Yuqun Chen Название: Grobner-shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra ISBN: 9814619485 ISBN-13(EAN): 9789814619486 Издательство: World Scientific Publishing Рейтинг: Цена: 19800.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations.
Emphasizing the search for patterns within and between biological sequences, trees, and graphs, Combinatorial Pattern Matching Algorithms in Computational Biology Using Perl and R shows how combinatorial pattern matching algorithms can solve computational biology problems that arise in the analysis of genomic, transcriptomic, proteomic, metabolomic, and interactomic data. It implements the algorithms in Perl and R, two widely used scripting languages in computational biology.
The book provides a well-rounded explanation of traditional issues as well as an up-to-date account of more recent developments, such as graph similarity and search. It is organized around the specific algorithmic problems that arise when dealing with structures that are commonly found in computational biology, including biological sequences, trees, and graphs. For each of these structures, the author makes a clear distinction between problems that arise in the analysis of one structure and in the comparative analysis of two or more structures. He also presents phylogenetic trees and networks as examples of trees and graphs in computational biology.
This book supplies a comprehensive view of the whole field of combinatorial pattern matching from a computational biology perspective. Along with thorough discussions of each biological problem, it includes detailed algorithmic solutions in pseudo-code, full Perl and R implementation, and pointers to other software, such as those on CPAN and CRAN.
Описание: This Book Is A Unique Work Which Provides An In-Depth Exploration Into The Mathematical Expertise, Philosophy, And Knowledge Of H W Gould. It Is Written In A Style That Is Accessible To The Reader With Basic Mathematical Knowledge, And Yet Contains Material That Will Be Of Interest To The Specialist In Enumerative Combinatorics. This Book Begins With Exposition On The Combinatorial And Algebraic Techniques That Professor Gould Uses For Proving Binomial Identities. These Techniques Are Then Applied To Develop Formulas Which Relate Stirling Numbers Of The Second Kind To Stirling Numbers Of The First Kind. Professor Gould'S Techniques Also Provide Connections Between Both Types Of Stirling Numbers And Bernoulli Numbers. Professor Gould Believes His Research Success Comes From His Intuition On How To Discover Combinatorial Identities.This Book Will Appeal To A Wide Audience And May Be Used Either As Lecture Notes For A Beginning Graduate Level Combinatorics Class, Or As A Research Supplement For The Specialist In Enumerative Combinatorics.
Описание: This book discusses cryptographic and combinatorial properties of Boolean functions. Boolean functions are very easy to understand (but deep in analysis) and the subject covers significant amount of material in digital circuits, communication theory, VLSI design, computer science, coding theory and Mathematics. Boolean function is considered as one of the most basic building blocks in cryptographic system design. The properties that make a Boolean function suitable for a cryptographic system, are mostly combinatorial. We discuss these properties (e.g., balancedness, nonlinearity, correlation immunity, propagation characteristics, algebraic immunity) in detail. For each of the properties, existing research results and the recent contributions in the literature will be presented. The basic material will always contain hardcore theoretical results. However, we present the materials in a way that a person with undergraduate level mathematical background can access it. Implementation details related to these properties (e.g., how to check in writing a program whether a Boolean function is correlation immune) will be detailed.In addition to theoretical construction techniques for Boolean functions with different combinatorial and cryptographic properties, the book will concentrate on different state-of-the-art search techniques. In some cases these search techniques provide better results than the construction techniques for low number of input variables and they are quite interesting as the size of the complete set of Boolean functions is super exponential in the number of input variables. Different symmetries in the set of Boolean functions will also be presented in detail. The author will present the inherent beauty of Boolean functions that he has experienced in his research career.
Автор: Yanpei Liu Название: Combinatorial Functional Equations: Advanced Theory ISBN: 3110624354 ISBN-13(EAN): 9783110624359 Издательство: Walter de Gruyter Цена: 33463.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The second volume mainly presents several kinds of meson functional equations which are divided into three types: outer, inner and surface. It is suited for a wide readership, including pure and applied mathematicians, and also computer scientists.
Автор: Yanpei Liu Название: Combinatorial Functional Equations: Basic Theory ISBN: 3110623919 ISBN-13(EAN): 9783110623918 Издательство: Walter de Gruyter Цена: 22491.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The first volume mainly presents basic concepts and the theoretical background. Differential (ordinary and partial) equations and relevant topics are discussed in detail.
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