Counting with Symmetric Functions

Szerző: Jeffrey Remmel, Anthony Mendes

Nyelv:

Kötés: Puha kötésű

Kiadó: Springer International Publishing AG

Elérhetőség: Beszállítói készleten

Küldés 5-8 napon belül

38 374 Ft

This monograph provides a self-contained introduction to symmetric functions and their use in enumer...

Információk a könyvről

Szerző

Jeffrey Remmel, Anthony Mendes

Nyelv

Angol

Kötés

Könyv - Puha kötésű

Kiadva

2019

oldal

292

EAN

9783319795102

Enbook ID

21072522

Kiadó

Springer International Publishing AG

Súly

468

Méretek

155 x 235 x 17

Teljes leírás

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.

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Counting with Symmetric Functions

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