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Developments in Mathematics

Counting with Symmetric Functions

Authors: Mendes, Anthony, Remmel, Jeffrey

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  • ​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
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eBook $84.99
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  • ISBN 978-3-319-23618-6
  • Digitally watermarked, DRM-free
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  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
Softcover $109.00
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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-Knuth algorithm 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)


Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-319-23618-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.00
price for USA in USD
Softcover $109.00
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Counting with Symmetric Functions
Authors
Series Title
Developments in Mathematics
Series Volume
43
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-23618-6
DOI
10.1007/978-3-319-23618-6
Hardcover ISBN
978-3-319-23617-9
Softcover ISBN
978-3-319-79510-2
Series ISSN
1389-2177
Edition Number
1
Number of Pages
X, 292
Number of Illustrations
209 b/w illustrations
Topics