"대칭다항식"의 두 판 사이의 차이
둘러보기로 가기
검색하러 가기
| 8번째 줄: | 8번째 줄: | ||
| − | algebraic independence result (Ruffini) | + | algebraic independence result (Ruffini, around 1800) |
| 36번째 줄: | 36번째 줄: | ||
\lambda : partition \lambda_1\ geq \lambda_2,\cdots, \lambda_n\geq 0 | \lambda : partition \lambda_1\ geq \lambda_2,\cdots, \lambda_n\geq 0 | ||
| − | + | <math>a_{\lambda+\delta}=\operatorname{det}(x_{i}^{\lambda_{j}+n-j})</math> | |
| + | |||
| + | |||
t_{\lambda} = det (h_{\lambda_{i}-i+j) | t_{\lambda} = det (h_{\lambda_{i}-i+j) | ||
2011년 11월 18일 (금) 09:09 판
polynomial symmetric functions
- three bases
- m
- e
- h
algebraic independence result (Ruffini, around 1800)
- power sums
- A. Girard
- Waring
반데몬드 행렬과 행렬식 (Vandermonde matrix)
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)