[组合] （z）一个排列组合问题

realnumber

浙江金华刘亮(38z----2)  09:16:34

2014-3-21 09:38

007

2014-3-21 11:30

2014-3-21 11:30

tommywong

$\begin{pmatrix}
0 & x12 & x13 & x14 & x15 & x16 & 0\\
x12 & 0 & x23 & x24 & x25 & x26 & 0\\
x13 & x23 & 0 & x34 & x35 & x36 & 0\\
x14 & x24 & x34 & 0 & x45 & x46 & 0\\
x15 & x25 & x35 & x45 & 0 & x56 & 0\\
x16 & x26 & x36 & x46 & x56 & 0 & 0
\end{pmatrix}=
\begin{pmatrix}
0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0\\
0 & 0 & 0 & 0 & 0 & 0 & 0
\end{pmatrix}=1
$

$\begin{pmatrix}
0 & x12 & x13 & x14 & x15 & x16 & 1\\
x12 & 0 & x23 & x24 & x25 & x26 & 1\\
x13 & x23 & 0 & x34 & x35 & x36 & 1\\
x14 & x24 & x34 & 0 & x45 & x46 & 1\\
x15 & x25 & x35 & x45 & 0 & x56 & 1\\
x16 & x26 & x36 & x46 & x56 & 0 & 1
\end{pmatrix}=5
\begin{pmatrix}
0 & x34 & x35 & x36 & 1\\
x34 & 0 & x45 & x46 & 1\\
x35 & x45 & 0 & x56 & 1\\
x36 & x46 & x56 & 0 & 1
\end{pmatrix}=15
\begin{pmatrix}
0 & x56 & 1\\
x56 & 0 & 1
\end{pmatrix}=15
$

$\begin{pmatrix}
0 & x12 & x13 & x14 & x15 & x16 & 2\\
x12 & 0 & x23 & x24 & x25 & x26 & 2\\
x13 & x23 & 0 & x34 & x35 & x36 & 2\\
x14 & x24 & x34 & 0 & x45 & x46 & 2\\
x15 & x25 & x35 & x45 & 0 & x56 & 2\\
x16 & x26 & x36 & x46 & x56 & 0 & 2
\end{pmatrix}=10
\begin{pmatrix}
0 & x23 & x24 & x25 & x26 & 1\\
x23 & 0 & x34 & x35 & x36 & 1\\
x24 & x34 & 0 & x45 & x46 & 2\\
x25 & x35 & x45 & 0 & x56 & 2\\
x26 & x36 & x46 & x56 & 0 & 2
\end{pmatrix}$

$=10(
\begin{pmatrix}
0 & x45 & x46 & 2\\
x45 & 0 & x56 & 2\\
x46 & x56 & 0 & 2
\end{pmatrix}+3
\begin{pmatrix}
0 & x34 & x35 & x36 & 1\\
x34 & 0 & x45 & x46 & 1\\
x35 & x45 & 0 & x56 & 2\\
x36 & x46 & x56 & 0 & 2
\end{pmatrix})=10(1+3(
\begin{pmatrix}
0 & x56 & 2\\
x56 & 0 & 2
\end{pmatrix}+2
\begin{pmatrix}
0 & x45 & x46 & 1\\
x45 & 0 & x56 & 1\\
x46 & x56 & 0 & 2
\end{pmatrix}))=10(1+3(2))=70
$

$\begin{pmatrix}
0 & x12 & x13 & x14 & x15 & x16 & 3\\
x12 & 0 & x23 & x24 & x25 & x26 & 3\\
x13 & x23 & 0 & x34 & x35 & x36 & 3\\
x14 & x24 & x34 & 0 & x45 & x46 & 3\\
x15 & x25 & x35 & x45 & 0 & x56 & 3\\
x16 & x26 & x36 & x46 & x56 & 0 & 3
\end{pmatrix}=10
\begin{pmatrix}
0 & x23 & x24 & x25 & x26 & 3\\
x23 & 0 & x34 & x35 & x36 & 3\\
x24 & x34 & 0 & x45 & x46 & 2\\
x25 & x35 & x45 & 0 & x56 & 2\\
x26 & x36 & x46 & x56 & 0 & 2
\end{pmatrix}$

$=10(
\begin{pmatrix}
0 & x45 & x46 & 0\\
x45 & 0 & x56 & 0\\
x46 & x56 & 0 & 0
\end{pmatrix}+3
\begin{pmatrix}
0 & x34 & x35 & x36 & 1\\
x34 & 0 & x45 & x46 & 1\\
x35 & x45 & 0 & x56 & 2\\
x36 & x46 & x56 & 0 & 2
\end{pmatrix}
)=10(1+3(
\begin{pmatrix}
0 & x56 & 2\\
x56 & 0 & 2
\end{pmatrix}+2
\begin{pmatrix}
0 & x45 & x46 & 1\\
x45 & 0 & x56 & 1\\
x46 & x56 & 0 & 2
\end{pmatrix}))
=10(1+3(2))=70
$

$\begin{pmatrix}
0 & x12 & x13 & x14 & x15 & x16 & 4\\
x12 & 0 & x23 & x24 & x25 & x26 & 4\\
x13 & x23 & 0 & x34 & x35 & x36 & 4\\
x14 & x24 & x34 & 0 & x45 & x46 & 4\\
x15 & x25 & x35 & x45 & 0 & x56 & 4\\
x16 & x26 & x36 & x46 & x56 & 0 & 4
\end{pmatrix}=5
\begin{pmatrix}
0 & x34 & x35 & x36 & 2\\
x34 & 0 & x45 & x46 & 2\\
x35 & x45 & 0 & x56 & 2\\
x36 & x46 & x56 & 0 & 2
\end{pmatrix}
=15
\begin{pmatrix}
0 & x56 & 0\\
x56 & 0 & 0
\end{pmatrix}=15
$