Bijective Combinatorics

Nicholas Loehr

February 10, 2011 by Chapman and Hall/CRC
Textbook - 612 Pages - 118 B/W Illustrations
ISBN 9781439848845 - CAT# K12206
Series: Discrete Mathematics and Its Applications

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  • Presents a readable yet rigorous exposition of enumerative combinatorics
  • Emphasizes bijective methods and combinatorial proofs
  • Requires minimal mathematical prerequisites
  • Includes a careful treatment of ranking, unranking, and successor algorithms
  • Provides detailed coverage of algebraic topics, such as formal power series, group actions, and symmetric polynomials, from a combinatorial viewpoint
  • Contains numerous worked examples and applications as well as nearly 1,000 exercises, ranging in difficulty from routine verifications to unsolved problems
  • Offers solutions, hints, or partial answers to many of the exercises at the end of the book

Errata and other pertinent information are available on the book’s website


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.