Download torrent Symmetric Functions and Combinatorial Operators on Polynomials

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Download torrent Symmetric Functions and Combinatorial Operators on Polynomials

Download torrent Symmetric Functions and Combinatorial Operators on Polynomials

Symmetric Functions and Combinatorial Operators on Polynomials .Alain Lascoux

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Author: Alain Lascoux
Page Count: 272 pages
Published Date: 15 Nov 2003
Publisher: American Mathematical Society
Publication Country: Providence, United States
Language: English
ISBN: 9780821828717
File size: 40 Mb
Download Link: Symmetric Functions and Combinatorial Operators on Polynomials
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The theory of symmetric functions is an old topic in mathematics which is used as an algebraic tool in many classical fields. With $lambda$-rings, one can regard symmetric functions as operators on polynomials and reduce the theory to just a handful of fundamental formulas. One of the main goals of the book is to describe the technique of $lambda$-rings. The main applications of this technique to the theory of symmetric functions are related to the Euclid algorithm and its occurrence in division, continued fractions, Pade approximants, and orthogonal polynomials. Putting the emphasis on the symmetric group instead of symmetric functions, one can extend the theory to non-symmetric polynomials, with Schur functions being replaced by Schubert polynomials. In two independent chapters, the author describes the main properties of these polynomials, following either the approach of Newton and interpolation methods or the method of Cauchy.The last chapter sketches a non-commutative version of symmetric functions, using Young tableaux and the plactic monoid. The book contains numerous exercises clarifying and extending many points of the main text. It will make an excellent supplementary text for a graduate course in combinatorics.

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