Graduate Texts in Mathematics

Lessons in Enumerative Combinatorics

Authors: Egecioglu, Omer, Garsia, Adriano

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  • 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
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eBook $59.99
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  • ISBN 978-3-030-71250-1
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Hardcover $79.99
price for USA in USD
  • ISBN 978-3-030-71249-5
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  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this Textbook

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.

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.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-3-030-71250-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA in USD
  • ISBN 978-3-030-71249-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Lessons in Enumerative Combinatorics
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
290
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-71250-1
DOI
10.1007/978-3-030-71250-1
Hardcover ISBN
978-3-030-71249-5
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XVI, 479
Number of Illustrations
326 b/w illustrations, 3 illustrations in colour
Topics