大葉大學圖書館 |

Counting with symmetric functions[electronic resource] /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.22
書名/作者:	Counting with symmetric functions/ by 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.
標題:	Sequences (Mathematics)
標題:	Functions, Special.
標題:	Combinatorial analysis.
標題:	Mathematics.
標題:	Combinatorics.
標題:	Special Functions.
標題:	Sequences, Series, Summability.
ISBN:	9783319236186
ISBN:	9783319236179
內容註:	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.
摘要、提要註:	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.
電子資源:	http://dx.doi.org/10.1007/978-3-319-23618-6

Counting with symmetric functions[electronic resource] /
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

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

635731
Symmetric functions.

LC Class. No.: QA212

Dewey Class. No.: 515.22

Counting with symmetric functions[electronic resource] /
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