网格的随机线性扩张
Random Linear Extensions of Grids
摘要：
格偏序集--或简称格--是链的乘积。我们会问，网格的随机线性扩展是什么样子的？特别是，我们表明，平均“跳跃数”，即，线性扩张中两个连续元素在偏序集中不可比的次数接近其最大可能值。所采用的技术依赖于熵参数。最后，我们提出几个关于这个开放领域的有趣问题。
英文摘要：
A grid poset -- or grid for short -- is a product of chains. We ask, what does a random linear extension of a grid look like? In particular, we show that the average "jump number," i.e., the number of times that two consecutive elements in a linear extension are incomparable in the poset, is close to its maximum possible value. The techniques employed rely on entropy arguments. We finish with several interesting questions about this wide-open area.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
