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Counting with symmetric functions [electronic resource]

Counting with symmetric functions [electronic resource]

Material type
E-Book(소장)
Personal Author
Remmel, Jeffrey B., 1948-. Mendes, Anthony.
Title Statement
Counting with symmetric functions [electronic resource] / Anthony Mendes, Jeffrey Remmel.
Publication, Distribution, etc
Cham :   Springer International Publishing :   Imprint: Springer,   2015.  
Physical Medium
1 online resource (x, 292 p.) : ill.
Series Statement
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.
General Note
Title from e-Book title page.  
Content Notes
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.
Bibliography, Etc. Note
Includes bibliographical references and index.
이용가능한 다른형태자료
Issued also as a book.  
Subject Added Entry-Topical Term
Symmetric functions. Counting.
Short cut
URL
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001 000046038620
005 20200730092947
006 m d
007 cr
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)

Holdings Information

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No. 1 Location Main Library/e-Book Collection/ Call Number CR 512.22 Accession No. E14028509 Availability Loan can not(reference room) Due Date Make a Reservation Service M

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