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- DescriptionBijective 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.
- Author BiographyNicholas A. Loehr teaches in the Department of Mathematics at Virginia Tech. His research interests include enumerative and algebraic combinatorics; symmetric and quasisymmetric functions; integer partitions, lattice paths, parking functions, and tableaux; bijective methods; and algorithm analysis.
- Author(s)Nicholas Loehr
- PublisherTaylor & Francis Ltd
- Date of Publication04/02/2011
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleDiscrete and Combinatorial Mathematics Series
- Series Part/Volume Number63
- Country of PublicationUnited States
- ImprintChapman & Hall/CRC
- Content Note118 black & white illustrations, 13 black & white tables
- Weight1247 g
- Width178 mm
- Height254 mm
- Spine33 mm
- Format DetailsUnsewn / adhesive bound
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