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[组合] 平面上n条直线交点数的所有可能

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hbghlyj posted 2019-10-2 16:29 |Read mode
平面上n条直线交点数的所有可能是0,1,n−1,n,n+1...$C_n^2$

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original poster hbghlyj posted 2019-10-2 16:41
回复 1# hbghlyj
设有$\lambda_i$条直线共点(i=1,2...k),$u_j$条直线平行(j=1,2...h),问题等价于:
$f(n)=\sum_{i=1}^kC^2_{\lambda_i-1}+\sum_{j=1}^hC_{u_j}^2$当i=1,2...k,j=1,2...h,$\lambda_i\geq3,\Sigma\lambda_i\leq n,\Sigma u_i\leq n$时跑遍$\{n+1,n+2\cdots C_n^2+2,C_n^2+n,C_n^2+n-1\}$

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