论文标题
Steiner三重系统的阈值
Threshold for Steiner triple systems
论文作者
论文摘要
我们证明，使用高概率$ \ mathbb {g}^{（3）}（n，n，n，n^{ - 1+o（1）}} $包含一个spanine steiner三重系统，用于$ n \ equiv 1,3 \ pmod {6} $，确定了theheshold概率的theheshold概率，以确定steiner theSiner theStriper theSteremence theStriple Systeence。我们还证明了拉丁正方形的类似定理。我们的结果来自一种新型的自举计划，该方案利用迭代吸收以及阈值与富兰克斯顿，卡恩，纳拉亚南和帕克建立的阈值与分数期望阈值之间的联系。
We prove that with high probability $\mathbb{G}^{(3)}(n,n^{-1+o(1)})$ contains a spanning Steiner triple system for $n\equiv 1,3\pmod{6}$, establishing the exponent for the threshold probability for existence of a Steiner triple system. We also prove the analogous theorem for Latin squares. Our result follows from a novel bootstrapping scheme that utilizes iterative absorption as well as the connection between thresholds and fractional expectation-thresholds established by Frankston, Kahn, Narayanan, and Park.
