슈르 다항식(Schur polynomial)

 

 

 

개요

• \(\rho : n-1,n-2,\cdots, 0\)
• \(\lambda: \lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n\geq 0\)
  \(a_{\lambda+\rho}=\operatorname{det}(x_{i}^{\lambda_{j}+n-j})\)
  \(t_{\lambda} = \frac{a_{\lambda+\rho}}{a_{\rho}} =\sum_{w\in S_{n} } \epsilon(w) h_{\lambda+\rho - w.\lambda}\)
  

 

 

 

\( s_\lambda(x_1,\ldots,x_n) = \sum_T w(T), \)

 

 

 

The first Giambelli formula (Jacobi-Trudy 항등식)

• explicit expression of Schur polynomials as a polynomial in the complete homogeneous symmetric polynomials:
• \(t_{\lambda} = \operatorname{det}(h_{\lambda_{i}-i+j})\)

 

 

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=