Overview
- Offers a unified and friendly approach to enumerative combinatorics through formal languages
- Showcases the authors' unique perspective and insightful examples
- Illuminates the important connection between discrete mathematics and computer science
- Engages readers through numerous exercises, examples, and applications
Part of the book series: Graduate Texts in Mathematics (GTM, volume 290)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
- Combinatorics
- bijective proofs
- generating functions
- planar trees
- Cayley trees
- Lagrange Inversion
- Inclusion-Exclusion Principle
- graph coloring
- determinantal formula
- combinatorics formal languages
- combinatorics graduate textbook
- combinatorics computer science
- exponential structures
- first available matching algorithm
- Adriano Garsia textbook
About this book
This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the 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; familiarity with linear algebra will enhance the study of certain chapters.
Reviews
“A whole book whose backbone is enumeration by codifying the objects to be enumerated as words. … They do this in a skillfully structured fashion which makes the connections natural and unforced. … One of the remarkable features of this book is the care the authors have taken to make it reader-friendly and accessible to a wide range of students following a graduatemathematics course or an honours undergraduate course in mathematics and computer science.” (Josef Lauri, zbMATH 1478.05001, 2022)
Authors and Affiliations
About the authors
Ömer Eğecioğlu is Professor of Computer Science at the University of California, Santa Barbara. His research interests include bijective and enumerative combinatorics, algorithms, and computational geometry.
Adriano Garsia is Professor Emeritus of Mathematics at the University of California, San Diego. He is renowned for his contributions to algebraic combinatorics, representation theory, and analysis. His wide-ranging research achievements are complemented by a lifelong enthusiasm for teaching and mentoring.
Together, the authors have previously published Lectures in Algebraic Combinatorics (2020) in the series Lecture Notes in Mathematics.
Bibliographic Information
Book Title: Lessons in Enumerative Combinatorics
Authors: Ömer Eğecioğlu, Adriano M. Garsia
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-030-71250-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-71249-5Published: 13 May 2021
Softcover ISBN: 978-3-030-71252-5Published: 14 May 2022
eBook ISBN: 978-3-030-71250-1Published: 13 May 2021
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVI, 479
Number of Illustrations: 326 b/w illustrations, 3 illustrations in colour
Topics: Discrete Mathematics, Mathematical Logic and Foundations, Mathematical Logic and Formal Languages