Combinatorics

ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly.

Combinatorics

Author: Robin J. Wilson

Publisher: Oxford University Press

ISBN: 0198723490

Page: 157

View: 752

How many possible sudoku puzzles are there? In the lottery, what is the chance that two winning balls have consecutive numbers? Who invented Pascal's triangle? (it was not Pascal) Combinatorics, the branch of mathematics concerned with selecting, arranging, and listing or counting collections of objects, works to answer all these questions. Dating back some 3000 years, and initially consisting mainly of the study of permutations and combinations, its scope has broadened to include topics such as graph theory, partitions of numbers, block designs, design of codes, and latin squares. In this Very Short Introduction Robin Wilson gives an overview of the field and its applications in mathematics and computer theory, considering problems from the shortest routes covering certain stops to the minimum number of colours needed to colour a map with different colours for neighbouring countries. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.

Combinatorics

A textbook in combinatorics for second-year undergraduate to beginning graduate students.

Combinatorics

Author: Peter J. Cameron

Publisher: Cambridge University Press

ISBN: 9780521457613

Page: 355

View: 535

A textbook in combinatorics for second-year undergraduate to beginning graduate students.

A Course in Combinatorics

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis.

A Course in Combinatorics

Author: J. H. van Lint

Publisher: Cambridge University Press

ISBN: 9780521006019

Page: 602

View: 245

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.

Surveys in Combinatorics 1995

This up-to-date survey of current research activity in several areas of combinatorics and its applications includes distance-regular graphs, combinatorial designs, coding theory, spectra of graphs, and randomness and computation.

Surveys in Combinatorics  1995

Author: British Combinatorial Conference

Publisher: Cambridge University Press

ISBN: 9780521497978

Page: 231

View: 217

This volume provides an up-to-date survey of current research activity in several areas of combinatorics and its applications. These include distance-regular graphs, combinatorial designs, coding theory, spectra of graphs, and randomness and computation. The articles give an overview of combinatorics that will be extremely useful to both mathematicians and computer scientists.

Combinatorics

This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, ...

Combinatorics

Author: Pavle Mladenović

Publisher: Springer

ISBN: 3030008312

Page: 365

View: 399

This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.

A Walk Through Combinatorics

This is a textbook for an introductory combinatorics course lasting one or two semesters.

A Walk Through Combinatorics

Author: Miklós Bóna

Publisher: World Scientific Publishing Company

ISBN: 9813148861

Page: 616

View: 250

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity. The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading. The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected] The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.

Combinatorics

A introductory guide to combinatorics, including reading questions and end-of-section exercises, suitable for undergraduate and graduate courses.

Combinatorics

Author: David R. Mazur

Publisher: MAA

ISBN: 9780883857625

Page: 391

View: 129

A introductory guide to combinatorics, including reading questions and end-of-section exercises, suitable for undergraduate and graduate courses.

Combinatorics and Commutative Algebra

Chapter III Further Aspects of Face Rings In this chapter we will briefly survey
some additional topics related to combinatorics and commutative algebra, mostly
dealing with the face ring of a simplicial complex. Our main focus will be on ...

Combinatorics and Commutative Algebra

Author: Richard P. Stanley

Publisher: Springer Science & Business Media

ISBN: 0817644334

Page: 168

View: 924

* Stanley represents a broad perspective with respect to two significant topics from Combinatorial Commutative Algebra: 1) The theory of invariants of a torus acting linearly on a polynomial ring, and 2) The face ring of a simplicial complex * In this new edition, the author further develops some interesting properties of face rings with application to combinatorics

Extremal Combinatorics

This is a concise, up-to-date introduction to extremal combinatorics for non-specialists.

Extremal Combinatorics

Author: Stasys Jukna

Publisher: Springer Science & Business Media

ISBN: 9783540663133

Page: 378

View: 255

This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.

Combinatorics The Art of Counting

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level.

Combinatorics  The Art of Counting

Author: Bruce E. Sagan

Publisher: American Mathematical Soc.

ISBN: 1470460327

Page: 304

View: 752

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Additive Combinatorics

The text is supplemented by a large number of exercises and new results.

Additive Combinatorics

Author: Terence Tao

Publisher: Cambridge University Press

ISBN: 1139458345

Page:

View: 392

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Enumerative Combinatorics Volume 1

An introduction, suitable for graduate students, showing connections to other areas of mathematics.

Enumerative Combinatorics  Volume 1

Author: Richard P. Stanley

Publisher: Cambridge University Press

ISBN: 9780521663519

Page: 340

View: 670

An introduction, suitable for graduate students, showing connections to other areas of mathematics.

Advanced Combinatorics

Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject.

Advanced Combinatorics

Author: Louis Comtet

Publisher: Springer Science & Business Media

ISBN: 9789027704412

Page: 343

View: 754

Notwithstanding its title, the reader will not find in this book a systematic account of this huge subject. Certain classical aspects have been passed by, and the true title ought to be "Various questions of elementary combina torial analysis". For instance, we only touch upon the subject of graphs and configurations, but there exists a very extensive and good literature on this subject. For this we refer the reader to the bibliography at the end of the volume. The true beginnings of combinatorial analysis (also called combina tory analysis) coincide with the beginnings of probability theory in the 17th century. For about two centuries it vanished as an autonomous sub ject. But the advance of statistics, with an ever-increasing demand for configurations as well as the advent and development of computers, have, beyond doubt, contributed to reinstating this subject after such a long period of negligence. For a long time the aim of combinatorial analysis was to count the different ways of arranging objects under given circumstances. Hence, many of the traditional problems of analysis or geometry which are con cerned at a certain moment with finite structures, have a combinatorial character. Today, combinatorial analysis is also relevant to problems of existence, estimation and structuration, like all other parts of mathema tics, but exclusively forjinite sets.

Surveys in Combinatorics 1991

This volume contains the invited papers presented at the British Combinatorial Conference, held at the University of Surrey in July 1991.

Surveys in Combinatorics  1991

Author: British Combinatorial Conference (1991, University of Surrey)

Publisher: Cambridge University Press

ISBN: 9780521407663

Page: 300

View: 603

This volume contains the invited papers presented at the British Combinatorial Conference, held at the University of Surrey in July 1991.

Probability and Combinatorics

This book covers a selection of topics on combinatorics, probability and discrete mathematics useful to the students of MCA, MBA, computer science and applied mathematics.

Probability and Combinatorics

Author: D.P. Apte

Publisher: Excel Books India

ISBN: 9788174465207

Page: 463

View: 296

This book covers a selection of topics on combinatorics, probability and discrete mathematics useful to the students of MCA, MBA, computer science and applied mathematics. The book uses a different approach in explaining these subjects, so as to be equally suitable for the students with different backgrounds from commerce to computer engineering. This book not only explains the concepts and provides variety of solved problems, but also helps students to develop insight and perception, to formulate and solve mathematical problems in a creative way. The book includes topics in combinatorics like advance principles of counting, combinatorial identities, concept of probability, random variables and their probability distributions, discrete and continuous standard distributions and jointly random variables, recurrence relations and generating functions. This book completely covers MCA syllabus of Pune University and will also be suitable for undergraduate science courses like B.Sc. as well as management courses.

Geometric Combinatorics

This text is a compilation of expository articles at the interface between combinatorics and geometry.

Geometric Combinatorics

Author: Ezra Miller

Publisher: American Mathematical Soc.

ISBN: 9780821886953

Page: 691

View: 806

Geometric combinatorics describes a wide area of mathematics that is primarily the study of geometric objects and their combinatorial structure. This text is a compilation of expository articles at the interface between combinatorics and geometry.