"영 태블로(Young tableau)"의 두 판 사이의 차이
Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
||
13번째 줄: | 13번째 줄: | ||
\end{array} | \end{array} | ||
$$ | $$ | ||
+ | |||
+ | |||
+ | ==영 태블로== | ||
+ | * 주어진 n의 분할에 대응되는 영 다이어그램에, $\{1,2,\cdots,n\}$ 을 채워넣어 얻어진다 | ||
+ | * 각 행과 열을 따라 이 수가 증가하는 영 태블로를 표준 영 태블로라 한다 | ||
2012년 12월 11일 (화) 11:21 판
개요
- 영 다이어그램 또는 Ferrers Diagram
영 다이어그램
- 자연수의 분할 $$\lambda: \lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n\geq 0$$
에 대응되는 다이어그램
- 7의 분할 $(4,2,1)$의 경우, 영 다이어그램은 다음과 같다
$$ \begin{array}{cccc} \square & \square & \square & \square \\ \square & \square & \text{} & \text{} \\ \square & \text{} & \text{} & \text{} \end{array} $$
영 태블로
- 주어진 n의 분할에 대응되는 영 다이어그램에, $\{1,2,\cdots,n\}$ 을 채워넣어 얻어진다
- 각 행과 열을 따라 이 수가 증가하는 영 태블로를 표준 영 태블로라 한다
표준 영 태블로
- 7의 분할 $(4,2,1)$의 영 다이어그램에 다음과 같은 수를 채워넣어 얻어진다
\begin{array}{ccc} \{1,4,6,7\} & \{2,5\} & \{3\} \\ \{1,3,6,7\} & \{2,5\} & \{4\} \\ \{1,2,6,7\} & \{3,5\} & \{4\} \\ \{1,3,6,7\} & \{2,4\} & \{5\} \\ \{1,2,6,7\} & \{3,4\} & \{5\} \\ \{1,4,5,7\} & \{2,6\} & \{3\} \\ \{1,3,5,7\} & \{2,6\} & \{4\} \\ \{1,2,5,7\} & \{3,6\} & \{4\} \\ \{1,3,4,7\} & \{2,6\} & \{5\} \\ \{1,2,4,7\} & \{3,6\} & \{5\} \\ \{1,2,3,7\} & \{4,6\} & \{5\} \\ \{1,3,5,7\} & \{2,4\} & \{6\} \\ \{1,2,5,7\} & \{3,4\} & \{6\} \\ \{1,3,4,7\} & \{2,5\} & \{6\} \\ \{1,2,4,7\} & \{3,5\} & \{6\} \\ \{1,2,3,7\} & \{4,5\} & \{6\} \\ \{1,4,5,6\} & \{2,7\} & \{3\} \\ \{1,3,5,6\} & \{2,7\} & \{4\} \\ \{1,2,5,6\} & \{3,7\} & \{4\} \\ \{1,3,4,6\} & \{2,7\} & \{5\} \\ \{1,2,4,6\} & \{3,7\} & \{5\} \\ \{1,2,3,6\} & \{4,7\} & \{5\} \\ \{1,3,4,5\} & \{2,7\} & \{6\} \\ \{1,2,4,5\} & \{3,7\} & \{6\} \\ \{1,2,3,5\} & \{4,7\} & \{6\} \\ \{1,2,3,4\} & \{5,7\} & \{6\} \\ \{1,3,5,6\} & \{2,4\} & \{7\} \\ \{1,2,5,6\} & \{3,4\} & \{7\} \\ \{1,3,4,6\} & \{2,5\} & \{7\} \\ \{1,2,4,6\} & \{3,5\} & \{7\} \\ \{1,2,3,6\} & \{4,5\} & \{7\} \\ \{1,3,4,5\} & \{2,6\} & \{7\} \\ \{1,2,4,5\} & \{3,6\} & \{7\} \\ \{1,2,3,5\} & \{4,6\} & \{7\} \\ \{1,2,3,4\} & \{5,6\} & \{7\} \end{array}
- 이렇게 얻어진 35개의 표준 영 태블로는 다음과 같다
\begin{array}{cccc} \boxed{1} & \boxed{4} & \boxed{6} & \boxed{7} \\ \boxed{2} & \boxed{5} & \text{} & \text{} \\ \boxed{3} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{6} & \boxed{7} \\ \boxed{2} & \boxed{5} & \text{} & \text{} \\ \boxed{4} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{6} & \boxed{7} \\ \boxed{3} & \boxed{5} & \text{} & \text{} \\ \boxed{4} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{6} & \boxed{7} \\ \boxed{2} & \boxed{4} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{6} & \boxed{7} \\ \boxed{3} & \boxed{4} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{4} & \boxed{5} & \boxed{7} \\ \boxed{2} & \boxed{6} & \text{} & \text{} \\ \boxed{3} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{5} & \boxed{7} \\ \boxed{2} & \boxed{6} & \text{} & \text{} \\ \boxed{4} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{5} & \boxed{7} \\ \boxed{3} & \boxed{6} & \text{} & \text{} \\ \boxed{4} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{4} & \boxed{7} \\ \boxed{2} & \boxed{6} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{4} & \boxed{7} \\ \boxed{3} & \boxed{6} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{7} \\ \boxed{4} & \boxed{6} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{5} & \boxed{7} \\ \boxed{2} & \boxed{4} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{5} & \boxed{7} \\ \boxed{3} & \boxed{4} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{4} & \boxed{7} \\ \boxed{2} & \boxed{5} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{4} & \boxed{7} \\ \boxed{3} & \boxed{5} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{7} \\ \boxed{4} & \boxed{5} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{4} & \boxed{5} & \boxed{6} \\ \boxed{2} & \boxed{7} & \text{} & \text{} \\ \boxed{3} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{5} & \boxed{6} \\ \boxed{2} & \boxed{7} & \text{} & \text{} \\ \boxed{4} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{5} & \boxed{6} \\ \boxed{3} & \boxed{7} & \text{} & \text{} \\ \boxed{4} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{4} & \boxed{6} \\ \boxed{2} & \boxed{7} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{4} & \boxed{6} \\ \boxed{3} & \boxed{7} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{6} \\ \boxed{4} & \boxed{7} & \text{} & \text{} \\ \boxed{5} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{4} & \boxed{5} \\ \boxed{2} & \boxed{7} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{4} & \boxed{5} \\ \boxed{3} & \boxed{7} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{5} \\ \boxed{4} & \boxed{7} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{4} \\ \boxed{5} & \boxed{7} & \text{} & \text{} \\ \boxed{6} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{5} & \boxed{6} \\ \boxed{2} & \boxed{4} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{5} & \boxed{6} \\ \boxed{3} & \boxed{4} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{4} & \boxed{6} \\ \boxed{2} & \boxed{5} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{4} & \boxed{6} \\ \boxed{3} & \boxed{5} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{6} \\ \boxed{4} & \boxed{5} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{3} & \boxed{4} & \boxed{5} \\ \boxed{2} & \boxed{6} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{4} & \boxed{5} \\ \boxed{3} & \boxed{6} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{5} \\ \boxed{4} & \boxed{6} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array},\begin{array}{cccc} \boxed{1} & \boxed{2} & \boxed{3} & \boxed{4} \\ \boxed{5} & \boxed{6} & \text{} & \text{} \\ \boxed{7} & \text{} & \text{} & \text{} \end{array}
사전 형태의 참고자료