论文标题
斯坦利（Stanley）的极端不平等现象
The extremals of Stanley's inequalities for partially ordered sets
论文作者
论文摘要
斯坦利（Stanley）对部分有序集的不平等现象为线性扩展计数序列建立了重要的对数洞穴关系。然而，他们的极端情况，即这些不平等现象的平等案例，直到现在，由于缺乏猜想，还没有理解。在这项工作中，我们通过提供史丹利不平等的极端表征来解决这个问题。我们的证明是基于在部分有序集合的组合和凸多属的几何形状之间构建新的``字典''，该组合捕获了其极端结构。
Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly understood with even conjectures lacking. In this work, we solve this problem by providing a complete characterization of the extremals of Stanley's inequalities. Our proof is based on building a new ``dictionary" between the combinatorics of partially ordered sets and the geometry of convex polytopes, which captures their extremal structures.
