Lessons in Enumerative Combinatorics

This textbook provides an introduction to enumerative combinatorics through the framework of formal languages and bijections,with numerous concrete examples and illustrative metaphors. It covers topics such as generating functions, partitions, Cayley trees, determinantal formulas, and the Inclusion-Exclusion Principle, and is suitable for students in mathematics and computer science at the graduate or advanced undergraduate level.

Format: Hardback
Length: 479 pages
Publication date: 13 May 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook offers a thorough introduction to enumerative combinatorics through the lens of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful and unified picture for readers entering this field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science.

Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley-Hamilton theorem.

The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications.

Lessons in Enumerative Combinatorics captures the authors distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed.

Weight: 994g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030712495
Edition number: 1st ed. 2021