Overview
- A self-contained introduction to symmetric functions and their use in counting problems
- First book to consider many of the methods and results presented
- Unifies a large number of results? in the theory of permutation enumeration
- Numerous exercises with full solutions included throughout
- Includes supplementary material: sn.pub/extras
Part of the book series: Developments in Mathematics (DEVM, volume 43)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (8 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
This monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas.
The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuthalgorithm and a method for proving Pólya’s enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties.
Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.
Reviews
“This book provides a current survey of techniques and applications of symmetric functions to enumeration theory, with emphasis on the combinatorics of the transition matrices between bases. … Each chapter ends with a substantial number of exercises along with full solutions, as well as accurate bibliographic notes. The book is definitely a very interesting addition to the literature on the subject.” (Domenico Senato, Mathematical Reviews, February, 2017)
“Though the authors target graduate students, advanced undergraduates will also surely have the necessary prerequisites, easily grasp the book's goals, and find many chapters accessible. … Summing Up: Recommended. Upper-division undergraduates through professionals/practitioners.” (D. V. Feldman, Choice, Vol. 53 (12), September, 2016)
Authors and Affiliations
Bibliographic Information
Book Title: Counting with Symmetric Functions
Authors: Anthony Mendes, Jeffrey Remmel
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-3-319-23618-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-23617-9Published: 04 December 2015
Softcover ISBN: 978-3-319-79510-2Published: 14 March 2019
eBook ISBN: 978-3-319-23618-6Published: 28 November 2015
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: X, 292
Number of Illustrations: 209 b/w illustrations
Topics: Combinatorics, Special Functions, Sequences, Series, Summability