Let denote the power set of [n], ordered by inclusion, and let denote the random poset obtained from by retaining each element from independently at random with probability p and discarding it otherwise. Given any fixed poset F we determine the threshold for the property that contains F as an induced subposet. We also asymptotically determine the number of copies of a fixed poset F in . Finally, we obtain a number of results on the Ramsey properties of the random poset .

中文翻译：

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随机坐姿的存在阈值和Ramsey性质

令[ n ]的幂集按包含顺序排序，并表示通过以概率p随机独立地保留每个元素并以其他方式丢弃它而获得的随机姿态。给定任何固定的姿态F，我们确定包含F作为诱导子姿态的属性的阈值。我们也渐近确定的固定偏序集的份数˚F在。最后，我们获得了有关随机坐姿Ramsey特性的许多结果。