作者：(澳)罗宾·兰格
页数：82
出版社：哈尔滨工业大学出版社
出版日期：2021
ISBN：9787560343839
电子书格式：PDF
PDF下载地址
内容简介
本书是一部英文版的数学专著,本书可以视为近代组合学中的一个小课题。
目录
1．Symmetric functions of Littlewood-Richardson type
1．1．Symmetric Functions
1．1．1．Partitions
1．1．2．Monomial syrmnetric functions
1．1．3．Plethystic notation
1．1．4．Schur functions
1．2．The Umbral Calculus
1．2．1．Coalgebras
1．2．2．Sequences of Binomial Type
1．3．The Hall inner-product
1．3．1．Preliminaries
1．3．2．Column operators
1．3．3．Duality
1．4．Littlewood-Richardson Bases
1．4．1．Generalized complete symmetric functions
1．4．2．Umbraloperators
1．4．3．Column operators
1．4．4．Generalized elementary symmetric functions
1．5．Examples
1．1．Symmetric Functions
1．1．1．Partitions
1．1．2．Monomial syrmnetric functions
1．1．3．Plethystic notation
1．1．4．Schur functions
1．2．The Umbral Calculus
1．2．1．Coalgebras
1．2．2．Sequences of Binomial Type
1．3．The Hall inner-product
1．3．1．Preliminaries
1．3．2．Column operators
1．3．3．Duality
1．4．Littlewood-Richardson Bases
1．4．1．Generalized complete symmetric functions
1．4．2．Umbraloperators
1．4．3．Column operators
1．4．4．Generalized elementary symmetric functions
1．5．Examples
2．A generating function identity for Macdonald polynomials
2．1．Macdonald Polynomials
2．1．1 ．Notation
2．1．2．Operator definition
2．1．3．Characterization using the inner product
2．1．4．Arms and legs
2．1．5．Duality
2．1．6．Kawanaka conjecture
2．2．Resultants
2．2．1．Residue calculations
2．3．Pieri formula and recurrence
2．3．1．Arms and legs again
2．3．2．Pieri formula
2．3．3．Recurrence
2．4．The Proof
2．4．1．The Schur case
2．4．2．Step one
2．4．3．Step two
2．4．4．Step three
References
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