A Walk Through Combinatorics
An Introduction to Enumeration, Graph Theory, and Selected Other TopicsThe first half of the book walks the reader through methods of counting, both direct elementary methods and the more advanced method of generating functions. Then, in the second half of the book, the reader learns how to apply these methods to fascinating objects, such as graphs, designs, random variables, partially ordered sets, and algorithms. In short, the first half emphasizes depth by discussing counting methods at length; the second half aims for breadth, by showing how numerous the applications of our methods are.New to this fifth edition of A Walk Through Combinatorics is the addition of Instant Check exercises ? more than a hundred in total ? which are located at the end of most subsections. As was the case for all previous editions, the exercises sometimes contain new material that was not discussed in the text, allowing instructors to spend more time on a given topic if they wish to do so. With a thorough introduction into enumeration and graph theory, as well as a chapter on permutation patterns (not often covered in other textbooks), this book is well suited for any undergraduate introductory combinatorics class.Contents: ForewordPrefaceAcknowledgmentsBasic Methods:Seven is More Than Six. The Pigeon-Hole PrincipleOne Step at a Time. The Method of Mathematical InductionEnumerative Combinatorics:There are a Lot of Them. Elementary Counting ProblemsNo Matter How You Slice It. The Binomial Theorem and Related IdentitiesDivide and Conquer. PartitionsNot So Vicious Cycles. Cycles in PermutationsYou Shall Not Overcount. The SieveA Function is Worth Many Numbers. Generating FunctionsGraph Theory:Dots and Lines. The Origins of Graph TheoryStaying Connected. TreesFinding a Good Match. Coloring and MatchingDo Not Cross. Planar GraphsHorizons:Does It Clique? Ramsey TheorySo Hard to Avoid. Subsequence Conditions on PermutationsWho Knows What It Looks Like, But It Exists. The Probabilistic MethodAt Least Some Order. Partial Orders and LatticesAs Evenly as Possible. Block Designs and Error Correcting CodesAre They Really Different? Counting Unlabeled StructuresThe Sooner the Better. Combinatorial AlgorithmsDoes Many Mean More Than One? Computational ComplexityBibliographyIndexReadership: This book is primarily suitable for advanced undergraduate students and instructors teaching an introductory combinatorics class. However, it would also be applicable to graduate students in fields other than combinatorics who need an introduction to Combinatorics.Review of the 4th Edition:’This is still one of the best introductions to combinatorics.’ – Mathematical Association of AmericaReview of the 3rd Edition:’The chapters on block designs and counting unlabeled structures have been added to the third edition, and there are also one hundred new problems in the other eighteen chapters. When I next teach a combinatorics course, this will be the text I use.’ – Mathematical ReviewsReviews of the 2nd Edition:’B?na’s book is an excellent choice for anyone who wants an introduction to this beautiful branch of mathematics ? Plentiful examples illustrate each of the topics included in the book. B?na does a supreme job of walking us through combinatorics.’ – CHOICE’This book covers all of the basic results one would expect and a selection of advanced topics as well. There are many very good problems in it. The problems in this book are, as the kids say, awesome. This is a comprehensive book on combinatorics. Exposition is clear, coverage is massive, and the problems are plentiful and excellent.’ – SIGACT NEWSKey Features: Includes a controlled access solutions manual as a resource for instructors who adopt the textbook The book contains a broad selection of other topics where the methods learned in the first part are applied The book contains a chapter on permutation patterns. This is not so in other introductory textbooks The goal of the author has been not simply that the reader learns about combinatorics, but also that the reader has fun while doing soISBN: 9789811277849, 9811277842
