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Combinatorics: First Steps, Volodymyr Vyshenskyi


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Автор: Volodymyr Vyshenskyi
Название:  Combinatorics: First Steps
ISBN: 9781685071523
Издательство: Nova Science
Классификация:
ISBN-10: 168507152X
Обложка/Формат: Hardback
Страницы: 338
Вес: 0.77 кг.
Дата издания: 05.11.2021
Серия: Mathematics
Язык: English
Размер: 157 x 230 x 28
Читательская аудитория: General (us: trade)
Ключевые слова: Combinatorics & graph theory
Подзаголовок: First steps
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Поставляется из: Англии
Описание: The main goal of our book is to provide easy access to the basic principles and methods that combinatorial calculations are based upon. The rule of product, the identity principle, recurrence relations and inclusion-exclusion principle are the most important of the above. Significant parts of the book are devoted to classical combinatorial structures, such as: ordering (permutations), tuples, and subsets (combinations). A great deal of attention is paid to the properties of binomial coefficients, and in particular, to model proofs of combinatorial identities. Problems concerning some exact combinatorial configurations such as paths in a square, polygonal chains constructed with chords of a circle, trees (undirected graphs with no cycles) etc. are included too. All chapters contain a considerable number of exercises of various complexity, from easy training tasks to complex problems which require decent persistence and skill from the one who dares to solve them. If one aims to passively familiarise oneself with the subject, methods and the most necessary facts of combinatorics, then it may suffice to limit ones study to the main text omitting the exercise part of the book. However, for those who want to immerse themselves in combinatorial problems and to gain skills of active research in that field, the exercise section is rather important. The authors hope that the book will be helpful for several categories of readers. University teachers and professors of mathematics may find somewhat unusual coverage of certain matters and exercises which can be readily applied in their professional work. We believe that certain series of problems may serve as a base for serious creative works and essays. This especially refers to students at pedagogical universities and colleges who need to prepare themselves to the teaching of the basics of combinatorics, mainly building on arithmetic and geometry. Most of the exercises of the book are of this very origin.

Analytic Combinatorics

Автор: Flajolet
Название: Analytic Combinatorics
ISBN: 0521898064 ISBN-13(EAN): 9780521898065
Издательство: Cambridge Academ
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Цена: 88710.00 T
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Описание: The definitive treatment of analytic combinatorics. This self-contained text covers the mathematics underlying the analysis of discrete structures, with thorough treatment of a large number of applications. Exercises, examples, appendices and notes aid understanding: ideal for individual self-study or for advanced undergraduate or graduate courses.

Enumerative Combinatorics

Автор: Stanley
Название: Enumerative Combinatorics
ISBN: 1107602629 ISBN-13(EAN): 9781107602625
Издательство: Cambridge Academ
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Цена: 39920.00 T
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Описание: Richard Stanley`s two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes more than 300 new exercises, many with solutions, updated and expanded chapter bibliographies and substantial new material on permutation statistics.

Introduction to Enumerative and Analytic Combinatorics

Автор: Bona Miklos
Название: Introduction to Enumerative and Analytic Combinatorics
ISBN: 148224909X ISBN-13(EAN): 9781482249095
Издательство: Taylor&Francis
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Цена: 88800.00 T
Наличие на складе: Нет в наличии.
Описание:

Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares.

Strengthening the analytic flavor of the book, this Second Edition:

  • Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions
  • Demonstrates powerful techniques that do not require the residue theorem or complex integration
  • Adds new exercises to all chapters, significantly extending coverage of the given topics

Introduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field.

Outstanding Academic Title of the Year, Choice magazine, American Library Association.


Algebraic Combinatorics

Автор: Richard P. Stanley
Название: Algebraic Combinatorics
ISBN: 1489992855 ISBN-13(EAN): 9781489992857
Издательство: Springer
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Цена: 37260.00 T
Наличие на складе: Поставка под заказ.
Описание: Written by an expert in the field, this undergraduate textbook will prepare the next generation of pure and applied mathematicians. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, and the Sperner property.

Algebraic Combinatorics and Computer Science

Автор: H. Crapo; D. Senato
Название: Algebraic Combinatorics and Computer Science
ISBN: 8847021596 ISBN-13(EAN): 9788847021594
Издательство: Springer
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Цена: 93160.00 T
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Описание: This book, dedicated to the memory of Gian-Carlo Rota, is the result of a collaborative effort by his friends, students and admirers. The book opens with a heartfelt piece by Henry Crapo in which he meticulously pieces together what Gian-Carlo Rota`s untimely demise has bequeathed to science.

Advanced Number Theory with Applications

Автор: Mollin
Название: Advanced Number Theory with Applications
ISBN: 1138113255 ISBN-13(EAN): 9781138113251
Издательство: Taylor&Francis
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Цена: 78590.00 T
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Описание:

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data.

With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat's Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue-Siegel-Roth theorem, Hall's conjecture, the Erd s-Mollin--Walsh conjecture, and the Granville-Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes', Selberg's, Linnik's, and Bombieri's sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring.

By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.


Algebraic combinatorics

Автор: Stanley, Richard P.
Название: Algebraic combinatorics
ISBN: 3319771728 ISBN-13(EAN): 9783319771724
Издательство: Springer
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Цена: 46570.00 T
Наличие на складе: Поставка под заказ.
Описание: Written by an expert in the field, this undergraduate textbook will prepare the next generation of pure and applied mathematicians. Key topics include walks on graphs, cubes and the Radon transform, the Matrix-Tree Theorem, and the Sperner property.

Advances in Combinatorics

Автор: Ilias S. Kotsireas; Eugene V. Zima
Название: Advances in Combinatorics
ISBN: 3642431755 ISBN-13(EAN): 9783642431753
Издательство: Springer
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Цена: 111790.00 T
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Описание:

This volume, as Andrew M. Odlzyko writes in the foreword, "commemorates and celebrates the life and achievements of an extraordinary person." Originally conceived as an 80th birthday tribute to Herbert Wilf, the well-known combinatorialist, the book has evolved beyond the proceeds of the W80 tribute.

Professor Wilf was an award-winning teacher, who was supportive of women mathematicians, and who had an unusually high proportion of women among his PhD candidates. He was Editor-in-chief of the American Mathematical Monthly and a founder of both the Journal of Algorithms and of the Electronic Journal of Combinatorics. But he was first a researcher, driven by his desire to know and explain the inner workings of the mathematical world.

The book collects high-quality, refereed research contributions by some of Professor Wilf's colleagues, students, and collaborators. Many of the papers presented here were featured in the Third Waterloo Workshop on Computer Algebra (WWCA 2011, W80), held May 26-29, 2011 at Wilfrid Laurier University, Waterloo, Canada. Others were included because of their relationship to his important work in combinatorics. All are presented as a tribute to Herb Wilf's contributions to mathematics and mathematical life.


Algebraic Combinatorics and Applications

Автор: Anton Betten; Axel Kohnert; Reinhard Laue; Alfred
Название: Algebraic Combinatorics and Applications
ISBN: 3540411100 ISBN-13(EAN): 9783540411109
Издательство: Springer
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Цена: 81050.00 T
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Описание: Proceedings of a high-level conference on discrete mathematics, focusing on group actions in the areas of pure mathematics, applied mathematics, computer science, physics, and chemistry. A useful tool for researchers and graduate students in discrete mathematics and theoretical computer science.

Advanced Combinatorics

Автор: Louis Comtet
Название: Advanced Combinatorics
ISBN: 9401021988 ISBN-13(EAN): 9789401021982
Издательство: Springer
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Цена: 81050.00 T
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Описание: The true beginnings of combinatorial analysis (also called combina- tory analysis) coincide with the beginnings of probability theory in the 17th century. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema- tics, but exclusively forjinite sets.

Buildings & Schubert Schemes

Автор: Contou-Carrere
Название: Buildings & Schubert Schemes
ISBN: 1498768296 ISBN-13(EAN): 9781498768290
Издательство: Taylor&Francis
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Цена: 193950.00 T
Наличие на складе: Нет в наличии.
Описание:

The first part of this book introduces the Schubert Cells and varieties of the general linear group Gl (k (r+1)) over a field k according to Ehresmann geometric way. Smooth resolutions for these varieties are constructed in terms of Flag Configurations in k (r+1) given by linear graphs called Minimal Galleries. In the second part, Schubert Schemes, the Universal Schubert Scheme and their Canonical Smooth Resolution, in terms of the incidence relation in a Tits relative building are constructed for a Reductive Group Scheme as in Grothendieck's SGAIII. This is a topic where algebra and algebraic geometry, combinatorics, and group theory interact in unusual and deep ways.


Using the Borsuk-Ulam Theorem / Lectures on Topological Methods in Combinatorics and Geometry

Автор: Matousek Jiri, BjГ¶rner A., Ziegler G.M.
Название: Using the Borsuk-Ulam Theorem / Lectures on Topological Methods in Combinatorics and Geometry
ISBN: 3540003622 ISBN-13(EAN): 9783540003625
Издательство: Springer
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Цена: 55890.00 T
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Описание: A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. They are scattered in research papers or outlined in surveys, and they often use topological notions not commonly known among combinatorialists or computer scientists.This book is the first textbook treatment of a significant part of such results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level (for example, homology theory and homotopy groups are completely avoided). No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained. This text started with a one-semester graduate course the author taught in fall 1993 in Prague. The transcripts of the lectures by the participants served as a basis of the first version. Some years later, a course partially based on that text was taught by GГјnter M. Ziegler in Berlin. The book is based on a thoroughly rewritten version prepared during a pre-doctoral course the author taught at the ETH Zurich in fall 2001.Most of the material was covered in the course: Chapter 1 was assigned as an introductory reading text, and the other chapters were presented in approximately 30 hours of teaching (by 45 minutes), with some omissions throughout and with only a sketchy presentation of the last chapter.


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