대칭다항식

polynomial symmetric functions

• three bases
  
  • m
  • e
  • h

 

algebraic independence result (Ruffini, around 1800)

 

• power sums
  
  • A. Girard
  • Waring

 

 

 

반데몬드 행렬과 행렬식 (Vandermonde matrix)

코 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} = det (h_{\lambda_{i}-i+j)

 

Schur polynomials

 

 

 

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