Download or read book A Survey of Combinatorial Theory written by Jagdish N. Srivastava and published by Elsevier. This book was released on 2014-05-12 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Survey of Combinatorial Theory covers the papers presented at the International Symposium on Combinatorial Mathematics and its Applications, held at Colorado State University (CSU), Fort Collins, Colorado on September 9-11, 1971. The book focuses on the principles, operations, and approaches involved in combinatorial theory, including the Bose-Nelson sorting problem, Golay code, and Galois geometries. The selection first ponders on classical and modern topics in finite geometrical structures; balanced hypergraphs and applications to graph theory; and strongly regular graph derived from the perfect ternary Golay code. Discussions focus on perfect ternary Golay code, finite projective and affine planes, Galois geometries, and other geometric structures. The book then examines the characterization problems of combinatorial graph theory, line-minimal graphs with cyclic group, circle geometry in higher dimensions, and Cayley diagrams and regular complex polygons. The text discusses combinatorial problems in finite Abelian groups, dissection graphs of planar point sets, combinatorial problems and results in fractional replication, Bose-Nelson sorting problem, and some combinatorial aspects of coding theory. The text also reviews the enumerative theory of planar maps, balanced arrays and orthogonal arrays, existence of resolvable block designs, and combinatorial problems in communication networks. The selection is a valuable source of information for mathematicians and researchers interested in the combinatorial theory.
Download or read book Problems in Combinatorics and Graph Theory written by Ioan Tomescu and published by Wiley-Interscience. This book was released on 1985-04-30 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the most important combinatorial structures and techniques. This is a book of problems and solutions which range in difficulty and scope from the elementary/student-oriented to open questions at the research level. Each problem is accompanied by a complete and detailed solution together with appropriate references to the mathematical literature, helping the reader not only to learn but to apply the relevant discrete methods. The text is unique in its range and variety -- some problems include straightforward manipulations while others are more complicated and require insights and a solid foundation of combinatorics and/or graph theory. Includes a dictionary of terms that makes many of the challenging problems accessible to those whose mathematical education is limited to highschool algebra.
Download or read book Combinatorial Problems and Exercises written by L. Lovász and published by Elsevier. This book was released on 2014-06-28 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book.Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.
Download or read book 102 Combinatorial Problems written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: "102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.
Download or read book Invitation to Discrete Mathematics written by Jiří Matoušek and published by Oxford University Press. This book was released on 2009 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear and self-contained introduction to discrete mathematics for undergraduates and early graduates.
Download or read book Some Problems in Combinatorial Theory written by Thomas Hustad Foregger and published by . This book was released on 1973 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorial Theory written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen
Download or read book Combinatorial Theory written by Marshall Hall and published by John Wiley & Sons. This book was released on 1998-07-16 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes proof of van der Waerden's 1926 conjecture on permanents, Wilson's theorem on asymptotic existence, and other developments in combinatorics since 1967. Also covers coding theory and its important connection with designs, problems of enumeration, and partition. Presents fundamentals in addition to latest advances, with illustrative problems at the end of each chapter. Enlarged appendixes include a longer list of block designs.
Download or read book Problems from the Discrete to the Continuous written by Ross G. Pinsky and published by Springer. This book was released on 2014-08-09 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
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.”
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.
Download or read book Graphical Enumeration written by Frank Harary and published by Elsevier. This book was released on 2014-05-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphical Enumeration deals with the enumeration of various kinds of graphs. Topics covered range from labeled enumeration and George Pólya's theorem to rooted and unrooted trees, graphs and digraphs, and power group enumeration. Superposition, blocks, and asymptotics are also discussed. A number of unsolved enumeration problems are presented. Comprised of 10 chapters, this book begins with an overview of labeled graphs, followed by a description of the basic enumeration theorem of Pólya. The next three chapters count an enormous variety of trees, graphs, and digraphs. The Power Group Enumeration Theorem is then described together with some of its applications, including the enumeration of self-complementary graphs and digraphs and finite automata. Two other chapters focus on the counting of superposition and blocks, while another chapter is devoted to asymptotic numbers that are developed for several different graphical structures. The book concludes with a comprehensive definitive list of unsolved graphical enumeration problems. This monograph will be of interest to both students and practitioners of mathematics.
Download or read book Combinatorics written by Robin J. Wilson and published by Oxford University Press. This book was released on 2016 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorics written by Pavle Mladenović and published by Springer. This book was released on 2019-03-13 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Path to Combinatorics for Undergraduates written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique approach to combinatorics is centered around unconventional, essay-type combinatorial examples, followed by a number of carefully selected, challenging problems and extensive discussions of their solutions. Topics encompass permutations and combinations, binomial coefficients and their applications, bijections, inclusions and exclusions, and generating functions. Each chapter features fully-worked problems, including many from Olympiads and other competitions, as well as a number of problems original to the authors; at the end of each chapter are further exercises to reinforce understanding, encourage creativity, and build a repertory of problem-solving techniques. The authors' previous text, "102 Combinatorial Problems," makes a fine companion volume to the present work, which is ideal for Olympiad participants and coaches, advanced high school students, undergraduates, and college instructors. The book's unusual problems and examples will interest seasoned mathematicians as well. "A Path to Combinatorics for Undergraduates" is a lively introduction not only to combinatorics, but to mathematical ingenuity, rigor, and the joy of solving puzzles.
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.
Download or read book Notes on Introductory Combinatorics written by George Polya and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the winter of 1978, Professor George P61ya and I jointly taught Stanford University's introductory combinatorics course. This was a great opportunity for me, as I had known of Professor P61ya since having read his classic book, How to Solve It, as a teenager. Working with P6lya, who ·was over ninety years old at the time, was every bit as rewarding as I had hoped it would be. His creativity, intelligence, warmth and generosity of spirit, and wonderful gift for teaching continue to be an inspiration to me. Combinatorics is one of the branches of mathematics that play a crucial role in computer sCience, since digital computers manipulate discrete, finite objects. Combinatorics impinges on computing in two ways. First, the properties of graphs and other combinatorial objects lead directly to algorithms for solving graph-theoretic problems, which have widespread application in non-numerical as well as in numerical computing. Second, combinatorial methods provide many analytical tools that can be used for determining the worst-case and expected performance of computer algorithms. A knowledge of combinatorics will serve the computer scientist well. Combinatorics can be classified into three types: enumerative, eXistential, and constructive. Enumerative combinatorics deals with the counting of combinatorial objects. Existential combinatorics studies the existence or nonexistence of combinatorial configurations.
