OPVSCVLVM · 001
Fixed Points of a Random Permutation
随机排列的不动点
A reconstruction of the mathematical note visible in a Bilibili video, accompanied by corrected, self-contained reports in English and Chinese.
Three editions
The reproduction preserves what appeared in the video. The two revised reports repair the mathematics and exposition, and stand on their own.
I / III
English · Reproduced
Source-faithful edition
A close typesetting of the four visible pages, intentionally preserving their unusual wording, omissions, notation, and induction calculation.
II / III
English · Revised
Corrected report
A self-contained treatment with a precise model, an inclusion–exclusion proof, a unified probability distribution, and an indicator-variable proof of the expectation.
III / III
中文 · 修订版
中文修订报告
与英文修订版内容一致的规范中文报告。该版采用相同的定义、结论与证明，并非对复刻版中不规范措辞的逐字翻译。
Source & purpose
Editorial note
This publication is an independent LaTeX reproduction of, and editorial adaptation based on, the paper shown in the Bilibili video linked below. The close reproduction is distinguished from the two corrected reports throughout.
It was prepared solely for entertainment and educational purposes. It is unofficial, is not presented as an author-approved transcript, and makes no claim of affiliation with the video creator or Bilibili.
【日常研究】摆烂小能手掀起的数学问题