Combinatorics

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Combinatorics: The Art of Counting

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorics

Author : Peter Jephson Cameron
Publisher : Cambridge University Press
ISBN 13 : 9780521457613
Total Pages : 372 pages
Book Rating : 4.4/5 (576 download)

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Book Synopsis Combinatorics by : Peter Jephson Cameron

Download or read book Combinatorics written by Peter Jephson Cameron and published by Cambridge University Press. This book was released on 1994-10-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorics for Computer Science

Author : Stanley Gill Williamson
Publisher : Courier Corporation
ISBN 13 : 9780486420769
Total Pages : 548 pages
Book Rating : 4.4/5 (27 download)

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Book Synopsis Combinatorics for Computer Science by : Stanley Gill Williamson

Download or read book Combinatorics for Computer Science written by Stanley Gill Williamson and published by Courier Corporation. This book was released on 2002-01-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.

Combinatorics

Author : Nicholas Loehr
Publisher : CRC Press
ISBN 13 : 149878027X
Total Pages : 979 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Combinatorics by : Nicholas Loehr

Download or read book Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2017-08-10 with total page 979 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

A Course in Combinatorics

Author : J. H. van Lint
Publisher : Cambridge University Press
ISBN 13 : 9780521006019
Total Pages : 620 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis A Course in Combinatorics by : J. H. van Lint

Download or read book A Course in Combinatorics written by J. H. van Lint and published by Cambridge University Press. This book was released on 2001-11-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics of Choice

Author : Ivan Niven
Publisher : MAA
ISBN 13 : 0883856158
Total Pages : 215 pages
Book Rating : 4.8/5 (838 download)

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Book Synopsis Mathematics of Choice by : Ivan Niven

Download or read book Mathematics of Choice written by Ivan Niven and published by MAA. This book was released on 1965 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Combinatorics

Author : Richard P. Stanley
Publisher : Springer Science & Business Media
ISBN 13 : 1461469988
Total Pages : 226 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Algebraic Combinatorics by : Richard P. Stanley

Download or read book Algebraic Combinatorics written by Richard P. Stanley and published by Springer Science & Business Media. This book was released on 2013-06-17 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Foundations of Combinatorics with Applications

Author : Edward A. Bender
Publisher : Courier Corporation
ISBN 13 : 0486151506
Total Pages : 738 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Foundations of Combinatorics with Applications by : Edward A. Bender

Download or read book Foundations of Combinatorics with Applications written by Edward A. Bender and published by Courier Corporation. This book was released on 2013-01-18 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.

Principles and Techniques in Combinatorics

Author : Chuan-Chong Chen
Publisher : World Scientific
ISBN 13 : 9789810211394
Total Pages : 314 pages
Book Rating : 4.2/5 (113 download)

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Book Synopsis Principles and Techniques in Combinatorics by : Chuan-Chong Chen

Download or read book Principles and Techniques in Combinatorics written by Chuan-Chong Chen and published by World Scientific. This book was released on 1992 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Applied Combinatorics

Author : Alan Tucker
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 408 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Applied Combinatorics by : Alan Tucker

Download or read book Applied Combinatorics written by Alan Tucker and published by John Wiley & Sons. This book was released on 1980 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Unity of Combinatorics

Author : Ezra Brown
Publisher : American Mathematical Soc.
ISBN 13 : 1470465094
Total Pages : 353 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Unity of Combinatorics by : Ezra Brown

Download or read book The Unity of Combinatorics written by Ezra Brown and published by American Mathematical Soc.. This book was released on 2021-04-05 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”

Combinatorics

Author : Béla Bollobás
Publisher : Cambridge University Press
ISBN 13 : 9780521337038
Total Pages : 196 pages
Book Rating : 4.3/5 (37 download)

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Book Synopsis Combinatorics by : Béla Bollobás

Download or read book Combinatorics written by Béla Bollobás and published by Cambridge University Press. This book was released on 1986-07-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.

Combinatorics and Graph Theory

Author : John Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387797114
Total Pages : 392 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Combinatorics and Graph Theory by : John Harris

Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Introduction to Combinatorics

Author : Martin J. Erickson
Publisher : John Wiley & Sons
ISBN 13 : 1118030893
Total Pages : 210 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Introduction to Combinatorics by : Martin J. Erickson

Download or read book Introduction to Combinatorics written by Martin J. Erickson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

Combinatorics and Random Matrix Theory

Author : Jinho Baik
Publisher : American Mathematical Soc.
ISBN 13 : 0821848410
Total Pages : 461 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Combinatorics and Random Matrix Theory by : Jinho Baik

Download or read book Combinatorics and Random Matrix Theory written by Jinho Baik and published by American Mathematical Soc.. This book was released on 2016-06-22 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last fifteen years a variety of problems in combinatorics have been solved in terms of random matrix theory. More precisely, the situation is as follows: the problems at hand are probabilistic in nature and, in an appropriate scaling limit, it turns out that certain key quantities associated with these problems behave statistically like the eigenvalues of a (large) random matrix. Said differently, random matrix theory provides a “stochastic special function theory” for a broad and growing class of problems in combinatorics. The goal of this book is to analyze in detail two key examples of this phenomenon, viz., Ulam's problem for increasing subsequences of random permutations and domino tilings of the Aztec diamond. Other examples are also described along the way, but in less detail. Techniques from many different areas in mathematics are needed to analyze these problems. These areas include combinatorics, probability theory, functional analysis, complex analysis, and the theory of integrable systems. The book is self-contained, and along the way we develop enough of the theory we need from each area that a general reader with, say, two or three years experience in graduate school can learn the subject directly from the text.

Counting and Configurations

Author : Jiri Herman
Publisher : Springer Science & Business Media
ISBN 13 : 1475739257
Total Pages : 402 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Counting and Configurations by : Jiri Herman

Download or read book Counting and Configurations written by Jiri Herman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents methods of solving problems in three areas of elementary combinatorial mathematics: classical combinatorics, combinatorial arithmetic, and combinatorial geometry. Brief theoretical discussions are immediately followed by carefully worked-out examples of increasing degrees of difficulty and by exercises that range from routine to rather challenging. The book features approximately 310 examples and 650 exercises.