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Other titles in the Discrete Mathematics and Its Applications series:
Bijective Combinatorics (Discrete Mathematics and Its Applications)by Nicholas A. Loehr
Synopses & Reviews
Book News Annotation:
In a textbook for an advanced undergraduate or beginning graduate course, Loehr (Virginia Polytechnic Institute and State University) presents a general introduction to enumerative combinatorics that emphasizes bijective methods. He explains the mathematical tools of basic counting rules, recursions, inclusion-exclusion, techniques, generating functions, bijective proofs, and linear algebraic methods then demonstrates how to used them to analyze many combinatorial structures. Most of the text requires no more mathematical background than basic logic, set theory, and proof techniques, but some sections assume some exposure to ideas from linear algebra. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)
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 tools, such as basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear-algebraic methods, needed to solve enumeration problems. These tools are used to analyze many combinatorial structures, including words, permutations, subsets, functions, compositions, integer partitions, graphs, trees, lattice paths, multisets, rook placements, set partitions, Eulerian tours, derangements, posets, tilings, and abaci. The book also delves into algebraic aspects of combinatorics, offering detailed treatments of formal power series, symmetric groups, group actions, symmetric polynomials, determinants, and the combinatorial calculus of tableaux. Each chapter includes summaries and extensive problem sets that review and reinforce the material.
Lucid, engaging, yet fully rigorous, this text describes a host of combinatorial techniques to help solve complicated enumeration problems. It covers the basic principles of enumeration, giving due attention to the role of bijective proofs in enumeration theory.
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