Bijective Combinatorics (Discrete Mathematics and Its Applications) 1st Edition by Nicholas Loehr (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐great item

⭐A delight, this book contains the entire program of a basic course in combinatorics. You will not regret purchasing. It is an excellent addition to your library!

⭐BC is not a bad entry in this important field but it is somewhat uneven. The exposition tends to beabbreviated toward the end – just when things are getting interesting – and the ‘solutions’at the back are a study in terseness. Perhaps a future edition can address these issues.

⭐A good book!

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