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000737583 019__ $$a931008196$$a931593441$$a932168922
000737583 020__ $$a9783319236186$$qelectronic book
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000737583 0247_ $$a10.1007/978-3-319-23618-6$$2doi
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000737583 08204 $$a515.22$$223
000737583 1001_ $$aMendes, Anthony,$$d1950-$$eauthor.
000737583 24510 $$aCounting with symmetric functions$$h[electronic resource] /$$cAnthony Mendes, Jeffrey Remmel.
000737583 264_1 $$aCham :$$bSpringer,$$c2015.
000737583 300__ $$a1 online resource.
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000737583 4901_ $$aDevelopments in mathematics ;$$vvolume 43
000737583 504__ $$aIncludes bibliographical references and index.
000737583 5050_ $$aPreface -- Permutations, Partitions, and Power Series -- Symmetric Functions -- Counting with the Elementary and Homogeneous -- Counting with a Nonstandard Basis -- Counting with RSK -- Counting Problems that Involve Symmetry -- Consecutive Patterns -- The Reciprocity Method -- Appendix: Transition Matrices -- References -- Index.
000737583 506__ $$aAccess limited to authorized users.
000737583 520__ $$aThis monograph provides a self-contained introduction to symmetric functions and their use in enumerative combinatorics. It is the first book to explore many of the methods and results that the authors present. Numerous exercises are included throughout, along with full solutions, to illustrate concepts and also highlight many interesting mathematical ideas. The text begins by introducing fundamental combinatorial objects such as permutations and integer partitions, as well as generating functions. Symmetric functions are considered in the next chapter, with a unique emphasis on the combinatorics of the transition matrices between bases of symmetric functions. Chapter 3 uses this introductory material to describe how to find an assortment of generating functions for permutation statistics, and then these techniques are extended to find generating functions for a variety of objects in Chapter 4. The next two chapters present the Robinson-Schensted-Knuth algorithm and a method for proving Pólya's enumeration theorem using symmetric functions. Chapters 7 and 8 are more specialized than the preceding ones, covering consecutive pattern matches in permutations, words, cycles, and alternating permutations and introducing the reciprocity method as a way to define ring homomorphisms with desirable properties. Counting with Symmetric Functions will appeal to graduate students and researchers in mathematics or related subjects who are interested in counting methods, generating functions, or symmetric functions. The unique approach taken and results and exercises explored by the authors make it an important contribution to the mathematical literature.
000737583 588__ $$aOnline resource; title from PDF title page (viewed December 16, 2015)
000737583 650_0 $$aSymmetric functions.
000737583 650_0 $$aSequences (Mathematics)
000737583 650_0 $$aFunctions, Special.
000737583 650_0 $$aCombinatorial analysis.
000737583 7001_ $$aRemmel, Jeffrey B.,$$d1948-$$eauthor.
000737583 77608 $$iPrint version:$$z9783319236179
000737583 830_0 $$aDevelopments in mathematics ;$$vvolume 43.
000737583 85280 $$bebk$$hSpringerLink
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