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Counting with symmetric functions [electronic resource]

Counting with symmetric functions [electronic resource]

자료유형
E-Book(소장)
개인저자
Remmel, Jeffrey B., 1948-. Mendes, Anthony.
서명 / 저자사항
Counting with symmetric functions [electronic resource] / Anthony Mendes, Jeffrey Remmel.
발행사항
Cham :   Springer International Publishing :   Imprint: Springer,   2015.  
형태사항
1 online resource (x, 292 p.) : ill.
총서사항
Developments in mathematics,1389-2177 ; 43
ISBN
9783319236186
요약
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.
일반주기
Title from e-Book title page.  
내용주기
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.
서지주기
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Symmetric functions. Counting.
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008 200728s2015 sz a ob 001 0 eng d
020 ▼a 9783319236186
040 ▼a 211009 ▼c 211009 ▼d 211009
050 4 ▼a QA164-167.2
082 0 4 ▼a 512.22 ▼2 23
084 ▼a 512.22 ▼2 DDCK
090 ▼a 512.22
100 1 ▼a Remmel, Jeffrey B., ▼d 1948-.
245 1 0 ▼a Counting with symmetric functions ▼h [electronic resource] / ▼c Anthony Mendes, Jeffrey Remmel.
260 ▼a Cham : ▼b Springer International Publishing : ▼b Imprint: Springer, ▼c 2015.
300 ▼a 1 online resource (x, 292 p.) : ▼b ill.
490 1 ▼a Developments in mathematics, ▼x 1389-2177 ; ▼v 43
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references and index.
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 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Symmetric functions.
650 0 ▼a Counting.
700 1 ▼a Mendes, Anthony.
830 0 ▼a Developments in mathematics ; ▼v 43.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-319-23618-6
945 ▼a KLPA
991 ▼a E-Book(소장)

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