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Counting with symmetric functions

Mendes, Anthony.

Counting with symmetric functions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Counting with symmetric functionsby Anthony Mendes, Jeffrey Remmel.
Author:	Mendes, Anthony.
other author:	Remmel, Jeffrey.
Published:	Cham :Springer International Publishing :2015.
Description:	x, 292 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Symmetric functions.
Online resource:	http://dx.doi.org/10.1007/978-3-319-23618-6
ISBN:	9783319236186$q(electronic bk.)

Counting with symmetric functions
Mendes, Anthony.

Counting with symmetric functions[electronic resource] /by Anthony Mendes, Jeffrey Remmel. - Cham :Springer International Publishing :2015. - x, 292 p. :ill., digital ;24 cm. - Developments in mathematics,v.431389-2177 ;. - Developments in mathematics ;v.25..

Preface -- Permutations, Partitions, and Power Series -- Symmetric Functions -- Counting with the Elementary and Homogeneous -- Counting with a Nonstandard Basis -- Counting with RSK -- Counting Problems that Involve Symmetry -- Consecutive Patterns -- The Reciprocity Method -- Appendix: Transition Matrices -- References -- Index.

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 Polya'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.

ISBN: 9783319236186$q(electronic bk.)

Standard No.: 10.1007/978-3-319-23618-6doiSubjects--Topical Terms:

245401
Symmetric functions.

LC Class. No.: QA212

Dewey Class. No.: 515.22

Counting with symmetric functions
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505 0 $a Preface -- Permutations, Partitions, and Power Series -- Symmetric Functions -- Counting with the Elementary and Homogeneous -- Counting with a Nonstandard Basis -- Counting with RSK -- Counting Problems that Involve Symmetry -- Consecutive Patterns -- The Reciprocity Method -- Appendix: Transition Matrices -- References -- Index.
520 $a 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 Polya'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.
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