Symmetric Functions and Combinatorial Operators on Polynomials is popular PDF and ePub book, written by Alain Lascoux in 2003, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Symmetric Functions and Combinatorial Operators on Polynomials can be Read Online from any device for your convenience.
Symmetric Functions and Combinatorial Operators on Polynomials Book PDF Summary
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 and the diagonalization of a kernel generalizing the resultant. The last chapter sketches a non-commutative version of symmetric functions, with the help of Young tableaux and the plactic monoid. The book also contains numerous exercises clarifying and extending many points of the main text.
Detail Book of Symmetric Functions and Combinatorial Operators on Polynomials PDF
- Author : Alain Lascoux
- Release : 20 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821828717
- Genre : Mathematics
- Total Page : 282 pages
- Language : English
- PDF File Size : 8,8 Mb
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