Counting with Symmetric Functions

Nonfiction, Science & Nature, Mathematics, Combinatorics, Mathematical Analysis
Cover of the book Counting with Symmetric Functions by Jeffrey Remmel, Anthony Mendes, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Jeffrey Remmel, Anthony Mendes ISBN: 9783319236186
Publisher: Springer International Publishing Publication: November 28, 2015
Imprint: Springer Language: English
Author: Jeffrey Remmel, Anthony Mendes
ISBN: 9783319236186
Publisher: Springer International Publishing
Publication: November 28, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer International Publishing

Cover of the book Methods of Fourier Analysis and Approximation Theory by Jeffrey Remmel, Anthony Mendes
Cover of the book Strengthening Teaching and Learning in Research Universities by Jeffrey Remmel, Anthony Mendes
Cover of the book Evidence-Based Implant Dentistry by Jeffrey Remmel, Anthony Mendes
Cover of the book EVOLVE – A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation VII by Jeffrey Remmel, Anthony Mendes
Cover of the book The Future of FinTech by Jeffrey Remmel, Anthony Mendes
Cover of the book Using Risk Analysis for Flood Protection Assessment by Jeffrey Remmel, Anthony Mendes
Cover of the book Religion, Crime and Punishment by Jeffrey Remmel, Anthony Mendes
Cover of the book Communications and Networking by Jeffrey Remmel, Anthony Mendes
Cover of the book The Force of Law Reaffirmed by Jeffrey Remmel, Anthony Mendes
Cover of the book Machine Learning in Medicine - Cookbook Three by Jeffrey Remmel, Anthony Mendes
Cover of the book Imagine Math 3 by Jeffrey Remmel, Anthony Mendes
Cover of the book War as Performance by Jeffrey Remmel, Anthony Mendes
Cover of the book Immersive Learning Research Network by Jeffrey Remmel, Anthony Mendes
Cover of the book Intelligent Human Computer Interaction by Jeffrey Remmel, Anthony Mendes
Cover of the book Mechanical Properties of Silicon Based Compounds: Silicides by Jeffrey Remmel, Anthony Mendes
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy