東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Counting with symmetric functions

Mendes, Anthony.

Linked to FindBook

Google Book

Amazon

博客來

Counting with symmetric functions

Record Type:	Electronic resources : Monograph/item
Title/Author:	Counting with symmetric functions/ by 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.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Symmetric functions. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-23618-6
ISBN:	9783319236186

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. 22..

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

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

550181
Symmetric functions.

LC Class. No.: QA212

Dewey Class. No.: 515.22

Counting with symmetric functions
LDR:02987nmm a2200325 a 4500 001 2013548
003 DE-He213
005 20160415133212.0
006 m d
007 cr nn 008maaau
008 160518s2015 gw s 0 eng d
020 $a 9783319236186 $q (electronic bk.)
020 $a 9783319236179 $q (paper)
024 7 $a 10.1007/978-3-319-23618-6 $2 doi
035 $a 978-3-319-23618-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA212
072 7 $a PBV $2 bicssc
072 7 $a MAT036000 $2 bisacsh
082 0 4 $a 515.22 $2 23
090 $a QA212 $b .M538 2015
100 1 $a Mendes, Anthony. $3 2163014
245 1 0 $a Counting with symmetric functions $h [electronic resource] / $c by Anthony Mendes, Jeffrey Remmel.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a x, 292 p. : $b ill., digital ; $c 24 cm.
490 1 $a Developments in mathematics, $x 1389-2177 ; $v v.43
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.
650 0 $a Symmetric functions. $3 550181
650 0 $a Sequences (Mathematics) $3 555869
650 0 $a Functions, Special. $3 606076
650 0 $a Combinatorial analysis. $3 523878
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Combinatorics. $3 895617
650 2 4 $a Special Functions. $3 897326
650 2 4 $a Sequences, Series, Summability. $3 897266
700 1 $a Remmel, Jeffrey. $3 2163015
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Developments in mathematics ; $v v. 22. $3 1325458
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-23618-6
950 $a Mathematics and Statistics (Springer-11649)