Counting with Symmetric Functions (Developments in Mathematics, 43) free ebook download.

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Counting with Symmetric Functions (Developments in Mathematics, 43) free ebook download

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Author(s):	Jeffrey Remmel

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	3319236172
Pages:	302	OCR:		Quality:		ISBN13:
Uploader:	maveriks	Upload Date:	2/28/2022 2:04:37 AM

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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 Plyas 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.
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3095970	Book	https://nitro.download/view/0709A46AB1BB...		0.00	maveriks

Tags: Counting Developments Functions Mathematics Symmetric

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