Combinatorics: Discrete Mathematics and its Applications

Combinatorics,Second Edition is a comprehensive introduction to enumerative,bijective,and algebraic combinatorics,with an emphasis on bijective proofs and accessible to readers without prior background in abstract algebra or combinatorics. It covers mathematical tools to solve counting problems and topics in algebraic combinatorics,with additional coverage of generating functions and examples and exercises.

Format: Paperback / softback
Length: 642 pages
Publication date: 21 January 2023
Publisher: Taylor & Francis Ltd

Combinatorics, Second Edition is a comprehensive and thorough introduction to the fields of enumerative, bijective, and algebraic combinatorics. The textbook places a strong emphasis on bijective proofs, which offer elegant solutions to counting problems by establishing one-to-one correspondences between two sets of combinatorial objects. The author has designed the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics.

Part I of the second edition introduces a diverse range of mathematical tools for solving counting problems. These tools encompass fundamental counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are employed to analyze various combinatorial structures, such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more.

Part II of the book delves into topics in algebraic combinatorics, including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition offers expanded coverage of the utilization of ordinary and exponential generating functions as problem-solving tools. In addition to two new chapters, numerous new sections, and enhanced exposition throughout, the textbook is replete with numerous examples and exercises of varying difficulty levels.

Combinatorics, Second Edition serves as an invaluable resource for students, researchers, and practitioners in the fields of mathematics, computer science, and related disciplines. Its comprehensive coverage, clear explanations, and abundant exercises make it an essential tool for anyone seeking to deepen their understanding of combinatorics and its applications.

Weight: 1190g
Dimension: 254 x 178 (mm)
ISBN-13: 9781032476711
Edition number: 2 ed