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Principles and Techniques in Combinatorics

Principles and Techniques in Combinatorics PDF Author: Chuan-Chong Chen
Publisher: World Scientific
ISBN: 9789810211394
Category : Mathematics
Languages : en
Pages : 314

Book Description
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.

Principles and Techniques in Combinatorics

Principles and Techniques in Combinatorics PDF Author: Chuan-Chong Chen
Publisher: World Scientific
ISBN: 9789810211394
Category : Mathematics
Languages : en
Pages : 314

Book Description
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.

Principles and Techniques in Combinatorics

Principles and Techniques in Combinatorics PDF Author: Lin Simon Mingyan
Publisher: World Scientific
ISBN: 9813238860
Category : Mathematics
Languages : en
Pages : 440

Book Description
The solutions to each problem are written from a first principles approach, which would further augment the understanding of the important and recurring concepts in each chapter. Moreover, the solutions are written in a relatively self-contained manner, with very little knowledge of undergraduate mathematics assumed. In that regard, the solutions manual appeals to a wide range of readers, from secondary school and junior college students, undergraduates, to teachers and professors.

Principles and Techniques in Combinatorics

Principles and Techniques in Combinatorics PDF Author: Chen Chuan-Chong
Publisher: World Scientific
ISBN: 981436567X
Category : Mathematics
Languages : en
Pages : 312

Book Description
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

Combinatorics PDF Author: Peter Jephson Cameron
Publisher: Cambridge University Press
ISBN: 9780521457613
Category : Mathematics
Languages : en
Pages : 372

Book Description
Combinatorics is a subject of increasing importance, owing to its links with computer science, statistics and algebra. This is a textbook aimed at second-year undergraduates to beginning graduates. It stresses common techniques (such as generating functions and recursive construction) which underlie the great variety of subject matter and also stresses the fact that a constructive or algorithmic proof is more valuable than an existence proof. The book is divided into two parts, the second at a higher level and with a wider range than the first. Historical notes are included which give a wider perspective on the subject. More advanced topics are given as projects and there are a number of exercises, some with solutions given.

A Course in Combinatorics

A Course in Combinatorics PDF Author: J. H. van Lint
Publisher: Cambridge University Press
ISBN: 9780521006019
Category : Mathematics
Languages : en
Pages : 620

Book Description
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

Combinatorics PDF Author: Nicholas Loehr
Publisher: CRC Press
ISBN: 149878027X
Category : Mathematics
Languages : en
Pages : 979

Book Description
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.

Bijective Combinatorics

Bijective Combinatorics PDF Author: Nicholas Loehr
Publisher: CRC Press
ISBN: 1439848866
Category : Computers
Languages : en
Pages : 600

Book Description
Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical

Basic Techniques of Combinatorial Theory

Basic Techniques of Combinatorial Theory PDF Author: Daniel I. A. Cohen
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 318

Book Description


Combinatorics: The Art of Counting

Combinatorics: The Art of Counting PDF Author: Bruce E. Sagan
Publisher: American Mathematical Soc.
ISBN: 1470460327
Category : Education
Languages : en
Pages : 304

Book Description
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.

Problem-Solving Methods in Combinatorics

Problem-Solving Methods in Combinatorics PDF Author: Pablo Soberón
Publisher: Springer Science & Business Media
ISBN: 3034805977
Category : Mathematics
Languages : en
Pages : 174

Book Description
Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book.​ The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.