zbMATH — the first resource for mathematics

Combinatorics. 2nd edition of the book previously published under the title Bijective combinatorics. (English) Zbl 1381.05001
Discrete Mathematics and Its Applications. Boca Raton, FL: CRC Press (ISBN 978-1-4987-8025-4/hbk; 978-1-4987-8026-1/ebook). xxiv, 618 p. (2018).
Publisher’s description: This book is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics.
Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more.
Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics.
This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
See the review of the first edition in [Zbl 1234.05001].

05-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics
05A19 Combinatorial identities, bijective combinatorics
05A15 Exact enumeration problems, generating functions
Zbl 1234.05001
Full Text: Link