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 Wilson

Publisher: Oxford University Press

ISBN: 0198723490

Page: 144

View: 423

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

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: 750

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.

Combinatorics A Guided Tour

This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ...

Combinatorics  A Guided Tour

Author: David R. Mazur

Publisher: American Mathematical Soc.

ISBN: 1470453002

Page: 390

View: 518

Combinatorics is mathematics of enumeration, existence, construction, and optimization questions concerning finite sets. This text focuses on the first three types of questions and covers basic counting and existence principles, distributions, generating functions, recurrence relations, Pólya theory, combinatorial designs, error correcting codes, partially ordered sets, and selected applications to graph theory including the enumeration of trees, the chromatic polynomial, and introductory Ramsey theory. The only prerequisites are single-variable calculus and familiarity with sets and basic proof techniques. The text emphasizes the brands of thinking that are characteristic of combinatorics: bijective and combinatorial proofs, recursive analysis, and counting problem classification. It is flexible enough to be used for undergraduate courses in combinatorics, second courses in discrete mathematics, introductory graduate courses in applied mathematics programs, as well as for independent study or reading courses. What makes this text a guided tour are the approximately 350 reading questions spread throughout its eight chapters. These questions provide checkpoints for learning and prepare the reader for the end-of-section exercises of which there are over 470. Most sections conclude with Travel Notes that add color to the material of the section via anecdotes, open problems, suggestions for further reading, and biographical information about mathematicians involved in the discoveries.

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: 195

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.

Combinatorics

Leading combinatorialists from around the world contributed to this volume.

Combinatorics

Author: A. Hajnal

Publisher: North-Holland

ISBN:

Page: 596

View: 717

Leading combinatorialists from around the world contributed to this volume. The plenary lecturers were the following: J. Beck (on combinatorial games), B. Bollobaacute;s (on cycles in random graphs), A. Brouwer (on extremal design theory), P. Erdodblac;s (on problems and results in combinatorics), C. Godsil (on the application of linear algebra in combinatorics), L. Lovaacute;sz (on matching theory), A.A. Razborov (on Boolean complexity), M. Saks (on collective coin flipping), and A. Schrijver (on disjoint paths in graphs).

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: 3662046504

Page: 378

View: 597

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 and Commutative Algebra

* 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 ...

Combinatorics and Commutative Algebra

Author: Richard P. Stanley

Publisher: Springer Science & Business Media

ISBN: 9780817643690

Page: 164

View: 965

The author is well known to the math community as an excellent researcher and expositor in the fields of combinatorics and algebra. His first book was widely read. In this second edition, which contains a significant amount of new material in areas of current interest, Stanley, as before, presents the "big picture" in an engaging framework.

Combinatorics

This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool.

Combinatorics

Author: Nicholas Loehr

Publisher: CRC Press

ISBN: 149878027X

Page: 618

View: 826

Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.

Principles and Techniques in Combinatorics

A textbook suitable for undergraduate courses.

Principles and Techniques in Combinatorics

Author: Chen Chuan-Chong

Publisher: World Scientific

ISBN: 981436567X

Page: 312

View: 264

A textbook suitable for undergraduate courses. The materials are presented very explicitly so that students will find it very easy to read. A wide range of examples, about 500 combinatorial problems taken from various mathematical competitions and exercises are also included. Contents:Permutations and CombinationsBinomial Coefficients and Multinomial CoefficientsThe Pigeonhole Principle and Ramsey NumbersThe Principle of Inclusion and ExclusionGenerating FunctionsRecurrence Relations Readership: Undergraduates, graduates and mathematicians. keywords:Binomial Coefficients;Multinomial Coefficients;Euler ϕ-Function;Enumerative Combinatorics;Addition Principle;Multiplication Principle;Combination;Permutation;Identities;Pigeon Hole Principle;Ramsey Numbers;Principle of Inclusion and Exclusion;Stirling Numbers;Derangements;Problem of Ménages;Sieve of Eratosthenes;Generating Functions;Partitions of Integers;Exponential Generating Functions;Recurrence Relations;Characteristic Polynomial;Catalan Numbers “This book should be a must for all mathematicians who are involved in the training of Mathematical Olympiad teams, but it will also be a valuable source of problems for university courses.” Mathematical Reviews

Combinatorics

This book is also ideal for readers who wish to better understand the various applications of elementary combinatorics.

Combinatorics

Author: Theodore G. Faticoni

Publisher: John Wiley & Sons

ISBN: 1118407482

Page: 328

View: 212

Bridges combinatorics and probability and uniquely includes detailed formulas and proofs to promote mathematical thinking Combinatorics: An Introduction introduces readers to counting combinatorics, offers examples that feature unique approaches and ideas, and presents case-by-case methods for solving problems. Detailing how combinatorial problems arise in many areas of pure mathematics, most notably in algebra, probability theory, topology, and geometry, this book provides discussion on logic and paradoxes; sets and set notations; power sets and their cardinality; Venn diagrams; the multiplication principal; and permutations, combinations, and problems combining the multiplication principal. Additional features of this enlightening introduction include: Worked examples, proofs, and exercises in every chapter Detailed explanations of formulas to promote fundamental understanding Promotion of mathematical thinking by examining presented ideas and seeing proofs before reaching conclusions Elementary applications that do not advance beyond the use of Venn diagrams, the inclusion/exclusion formula, the multiplication principal, permutations, and combinations Combinatorics: An Introduction is an excellent book for discrete and finite mathematics courses at the upper-undergraduate level. This book is also ideal for readers who wish to better understand the various applications of elementary combinatorics.

Combinatorics The Rota Way

Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.

Combinatorics  The Rota Way

Author: Joseph P. S. Kung

Publisher: Cambridge University Press

ISBN: 052188389X

Page: 396

View: 647

Compiled and edited by two of Gian-Carlo Rota's students, this book is based on notes from his influential combinatorics courses.

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: 254

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

Combinatorics

The book expounds on the general rules of combinatorics, the rule of sum, the rule of product, samples, permutations, combinations, and arrangements of subjects with various restrictions.

Combinatorics

Author: N. Ya. Vilenkin

Publisher: Academic Press

ISBN: 1483266117

Page: 314

View: 392

Combinatorics deals with simple combinatorial problems, recurrence relations, and generating functions, particularly the binomial expansions. The book expounds on the general rules of combinatorics, the rule of sum, the rule of product, samples, permutations, combinations, and arrangements of subjects with various restrictions. The text also explains ordered or unordered partitions of numbers, geometric methods, random walk problems, and variants of the arithmetical triangle. One example of the use of combinatorics is the choice of the number 3 in the genetic code. Another example involves the choice of crew for a spaceship where it is necessary to consider the psychological conditions of the applicants for space travel. The text also investigates the sieve of Erastothenes whose problem concerns finding all the primes in the sequence of natural numbers from 1 to N. The book also tackles the application of power series to proof of identities, the binomial series expansion, decomposition into elementary fractions, and nonlinear recurrence relation. The book can be highly educational and interesting to students or academicians involved in mathematics, algebra, and statistics.

50 years of Combinatorics Graph Theory and Computing

The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering.

50 years of Combinatorics  Graph Theory  and Computing

Author: Fan Chung

Publisher: CRC Press

ISBN: 1000752097

Page: 416

View: 558

50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science. Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter

A Walk Through Combinatorics

The subject of combinatorics is so vast that the author of a textbook faces a
difficult decision as to what topics to include. There is no more-or-less canonical
corpus as in such other subjects as number theory and complex variable theory.

A Walk Through Combinatorics

Author: Mikl¢s B¢na

Publisher: World Scientific

ISBN: 9812568859

Page: 469

View: 582

This is a textbook for an introductory combinatorics course that can take up 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 edition, 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 for the talented and hard-working 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 and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

Combinatorics

This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973.

Combinatorics

Author: T. P. McDonough

Publisher: Cambridge University Press

ISBN: 0521204542

Page: 204

View: 981

This volume is a record of the papers presented to the fourth British Combinatorial Conference held in Aberystwyth in July 1973. Contributors from all over the world took part and the result is a very useful and up-to-date account of what is happening in the field of combinatorics. A section of problems illustrates some of the topics in need of further investigation.

Horizons of Combinatorics

The collection gives an overview of recent trends and results in a large part of combinatorics and related topics.

Horizons of Combinatorics

Author: Ervin Gyori

Publisher: Springer Science & Business Media

ISBN: 3540772006

Page: 280

View: 579

Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry. The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives an overview of recent trends and results in a large part of combinatorics and related topics.

Enumerative Combinatorics Volume 2

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

Enumerative Combinatorics  Volume 2

Author: Richard P. Stanley

Publisher: Cambridge University Press

ISBN: 9780521789875

Page: 600

View: 742

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

Algebraic Combinatorics

The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory.

Algebraic Combinatorics

Author: Richard P. Stanley

Publisher: Springer Science & Business Media

ISBN: 1461469988

Page: 223

View: 305

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.