考虑purfer序列,若生成树的pufer序列为$p_{i}$,则答案为$(\prod_{i=1}^{n}a_{i})\sum_{p}\prod_{i=1}^{n}\frac{(a_{i}-1)!}{(a_{i}-1-s_{i})!}$(其中$s_{i}$为$p$中点$i$出现的次数,即度数减1) (以下令$a_{i}$减1)观察到式子只与$s_{i}$有关,对于相同的$s_{i}$对应$p_{i}$有$\frac{(n-2)!}{\prod_{i=1}^{n}s_{i}!}$种,令$C=(n-…

Lists of tables and figures A list of the tables and figures keep the information organized and provide easy access to a specific element. This article explains how to create a list of figures, a list of tables and how to change the default title in…

原文:http://www.mathworks.com/support/bugreports/1293244 Description Deployed GUIs and figures look and feel different compared to undeployed MATLAB desktop versions. Deployed applications are using the cross platform look and feel by default, while th…

Figures To insert a figure in a LaTeX document, you write lines like this: \begin{figure} \centering \includegraphics[width=3.0in]{imagefile1} \caption{Caption for figure} \label{fig:sample_figure} \end{figure} The whole block is enclosed between \be…

响应式图像 Bootstrap中的图像响应 .img-fluid <img class="img-fluid" src="http://lorempixel.com/1024/580/business" alt=""> 图像会随着父元素一起缩放 圆角边框 使用.img-thumbnail为图像提供圆形1px边框外观 <img class="img-fluid img-thumbnail" src="…

Figures Inscribed in Curves\text{Figures Inscribed in Curves}Figures Inscribed in Curves A short tour of an old problem by Mark J. Nielsen (Professor of Mathematics, University of Idaho) These pages give a brief and informal introduction to one of my…

The math faculty of Berland State University has suffered the sudden drop in the math skills of enrolling students. This year the highest grade on the entrance math test was 8. Out of 100! Thus, the decision was made to make the test easier. Future s…

\renewcommand{\thetable}{S\arabic{table}} \renewcommand{\thefigure}{S\arabic{figure}} 这样就以Table S1, Table S2... Figure S1, Figure S2编码了.…

有一个\(2^k\cdot 2^k\) 的全零矩阵 \(M\),给出 \(2^k\cdot 2^k\) 的 \(01\) 矩阵 \(F\),现在可以将 \(F\) 的左上角置于 \(M\) 的任一位置(超出部分就循环,\(2^k\) 的下一个就是 \(1\)),然后相应位置相异或.现在可以执行任意次以上操作:将 \(F\)放于某个位置,执行对应的异或操作.问最后不同的 \(M\)有多少个. Solution 很显然我们可以 \(F\) 放在每一个位置的异或结果都算出来,放在一起,变成一个集合,那…

考虑一个构造:令初始$2^{k}\times 2^{k}$的矩阵为$A$(下标从0开始),再构造一个矩阵$T$,满足仅有$T_{x_{i},y_{i}}=1$(其余位置都为0),定义矩阵卷积$\otimes$即$$(A\otimes B)_{x,y}=\bigoplus_{x_{1}+x_{2}\equiv x(mod\ 2^{k}),y_{1}+y_{2}\equiv y(mod\ 2^{k})}A_{x_{1},y_{1}}B_{x_{2},y_{2}}$$(不难证明这个卷积运算有交换律和结…