Combinatorics: The Art of Counting
About this Title
Bruce E. Sagan, Michigan State University, East Lansing, MI
Publication: Graduate Studies in Mathematics
Publication Year: 2020; Volume 210
ISBNs: 978-1-4704-6032-7 (print); 978-1-4704-6280-2 (online)
This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance.
The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.
Undergraduate and graduate students interested in combinatorics.
Table of Contents
- Basic counting
- Counting with signs
- Counting with ordinary generating functions
- Counting with exponential generating functions
- Counting with partially ordered sets
- Counting with group actions
- Counting with symmetric functions
- Counting with quasisymmetric functions
- Introduction to representation theory