대칭다항식

 

 

개요

 

• polynomial symmetric functions
• three well-known bases
  
  • m : monomial symmetric functions
  • e :  elementary symmetric polynomials
  • h :  complete homogeneous symmetric polynomials

 

• algebraic independence result (Ruffini, around 1800)

 

• power sums
  
  • A. Girard
  • Waring

 

 

 

반데몬드 행렬과 행렬식 (Vandermonde matrix)

코쉬 행렬과 행렬식

 

 

 

Jacobi-Trudi identity

sequence \delta : n-1,n-2,\cdots, 0

\lambda : partition \lambda_1\ geq \lambda_2,\cdots, \lambda_n\geq 0

\(a_{\lambda+\delta}=\operatorname{det}(x_{i}^{\lambda_{j}+n-j})\)

\(t_{\lambda} = a_{\lambda+\delta}/a_{\delta} =\sum_{w\in S_{n} } \epsilon(w) h_{\lambda+\delta - w.\lambda}\)

 

 

The first Giambelli formula

\(t_{\lambda} = \operatorname{det}(h_{\lambda_{i}-i+j})\)

 

Schur polynomials http://en.wikipedia.org/wiki/Schur_polynomial

 

 

 

J. Dieudonné, Schur functions and group representations , Young tableaux and Schur functors in algebra and geometry, Astéerisque, 87--88 , 7--19 (1981)

 

 

 

 

역사

 

• http://www.google.com/search?hl=en&tbs=tl:1&q=
• 수학사연표

 

 

메모

 

• Math Overflow http://mathoverflow.net/search?q=

 

 

 

 

수학용어번역

• 단어사전
  
  • http://translate.google.com/#en%7Cko%7C
  • http://ko.wiktionary.org/wiki/
• 발음사전 http://www.forvo.com/search/
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 한국통계학회 통계학 용어 온라인 대조표
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• The Online Encyclopaedia of Mathematics
• NIST Digital Library of Mathematical Functions
• The World of Mathematical Equations

 

 

 

 

 

관련논문

• http://www.jstor.org/action/doBasicSearch?Query=
• http://www.ams.org/mathscinet
• http://dx.doi.org/

 

 

관련도서

• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=