Counting with Symmetric Functions

Counting with Symmetric Functions
Author :
Publisher : Birkhäuser
Total Pages : 297
Release :
ISBN-10 : 9783319236186
ISBN-13 : 3319236180
Rating : 4/5 (180 Downloads)

Book Synopsis Counting with Symmetric Functions by : Jeffrey Remmel

Download or read book Counting with Symmetric Functions written by Jeffrey Remmel and published by Birkhäuser. This book was released on 2015-11-28 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


Counting with Symmetric Functions Related Books

Counting with Symmetric Functions
Language: en
Pages: 297
Authors: Jeffrey Remmel
Categories: Mathematics
Type: BOOK - Published: 2015-11-28 - Publisher: Birkhäuser

DOWNLOAD EBOOK

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
Combinatorics: The Art of Counting
Language: en
Pages: 328
Authors: Bruce E. Sagan
Categories: Education
Type: BOOK - Published: 2020-10-16 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In add
An Introduction to Symmetric Functions and Their Combinatorics
Language: en
Pages: 359
Authors: Eric S. Egge
Categories: Education
Type: BOOK - Published: 2019-11-18 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This book is a reader-friendly introduction to the theory of symmetric functions, and it includes fundamental topics such as the monomial, elementary, homogeneo
Notes on Counting: An Introduction to Enumerative Combinatorics
Language: en
Pages: 235
Authors: Peter J. Cameron
Categories: Mathematics
Type: BOOK - Published: 2017-06-29 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

An introduction to enumerative combinatorics, vital to many areas of mathematics. It is suitable as a class text or for individual study.
The $q,t$-Catalan Numbers and the Space of Diagonal Harmonics
Language: en
Pages: 178
Authors: James Haglund
Categories: Mathematics
Type: BOOK - Published: 2008 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This work contains detailed descriptions of developments in the combinatorics of the space of diagonal harmonics, a topic at the forefront of current research i