國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Counting with symmetric functions

Mendes, Anthony.

Counting with symmetric functions

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Counting with symmetric functionsby Anthony Mendes, Jeffrey Remmel.
作者:	Mendes, Anthony.
其他作者:	Remmel, Jeffrey.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	x, 292 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Symmetric functions.
電子資源:	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
LDR:02987nmm a2200325 a 4500 001 476970
003 DE-He213
005 20160415133212.0
006 m d
007 cr nn 008maaau
008 160526s2015 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 731779
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 245401
650 0 $a Sequences (Mathematics) $3 228268
650 0 $a Functions, Special. $3 281573
650 0 $a Combinatorial analysis. $3 182280
650 1 4 $a Mathematics. $3 184409
650 2 4 $a Combinatorics. $3 274788
650 2 4 $a Special Functions. $3 274846
650 2 4 $a Sequences, Series, Summability. $3 275704
700 1 $a Remmel, Jeffrey. $3 731780
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Developments in mathematics ; $v v.25. $3 558834
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-23618-6
950 $a Mathematics and Statistics (Springer-11649)