Counting with symmetric functions [electronic resource] / Anthony Mendes, Jeffrey Remmel.
2015
QA212
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Details
Title
Counting with symmetric functions [electronic resource] / Anthony Mendes, Jeffrey Remmel.
ISBN
9783319236186 electronic book
3319236180 electronic book
9783319236179
3319236172
3319236180 electronic book
9783319236179
3319236172
Published
Cham : Springer, 2015.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-319-23618-6 doi
Call Number
QA212
Dewey Decimal Classification
515.22
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file PDF
Source of Description
Online resource; title from PDF title page (viewed December 16, 2015)
Added Author
Remmel, Jeffrey B., 1948- author.
Series
Developments in mathematics ; volume 43.
Available in Other Form
Print version: 9783319236179
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Online Access
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Table of Contents
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.
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.