学术报告

       报告: Saturation results around the Erdős--Szekeres problem

       时间：2024年11月04日14：00-15：00

       地点：长安校区理学院楼 315

       邀请人：李若楠

       摘要：We consider saturation problems related to the celebrated Erdős--Szekeres convex polygon problem. For each $n \ge 7$, we construct a planar point set of size $(7/8) \cdot 2^{n-2}$ which is saturated for convex $n$-gons. That is, the set contains no $n$ points in convex position while the addition of any new point creates such a configuration. This demonstrates that the saturation number is smaller than the Ramsey number for the Erdős--Szekeres problem. The proof also shows that the original Erdős--Szekeres construction is indeed saturated. The construction is based on a similar improvement for the saturation version of the cups-versus-caps theorem. Moreover, we consider the generalization of the cups-versus-caps theorem to monotone paths in ordered hypergraphs. In contrast to the geometric setting, we show that this abstract saturation number is always equal to the corresponding Ramsey number.

       报告人简介：董子超，韩国基础科学研究院博士后，合作导师为刘鸿教授。2023年获得美国卡耐基梅隆大学博士学位。主要从事极值组合学方面的研究，目前有2篇成果发表在《SIAM Journal on Discrete Mathematics》。