Erdos-Ko-Rado theorem and Kruskal-Katona Theorem

Erdos-Ko-Rado theorem and Kruskal-Katona Theorem 活动信息 开始时间：2024-10-23 16:00:00 活动地点：创客基地楼 114 主讲人：王军 10 23 16:00 活动简介 <p>In the late 1960's, Kruskal and Katona solved independently an isoperimetric problem in the high-dimensional simplex. A general Kruskal-Katona-type problem on graphs is to describe subsets of the vertex set of a graph with minimum number of neighborhoods with respect to its their own sizes. We reort a few of Kruskal-Katona-type theorems for graphs, especially for the derangement graph of the symmetric group on a finite set. With this theorem we deduce the size and structure of the first three maximal intersecting families in the symmetric group, where the first was given by Deza-Frankl and Cameron-Ku; the second was conjectured by Cameron-Ku. With this theorem we also determine the maximum product of two cross-intersecting families in the symmetric group under various conditions.</p> 主讲人介绍 王军，上海师范大学数理学院教授， 曾任中国数学会组合与图论专业委员会副主任（2006-2018）以及上海师范大学数理学院学术委员会主任等职。 主要的研究领域是组合数学，特别是有限集及有限偏序集的组合学，解决了其中一些引人注目的问题和猜想。曾多次参加或主持国家级和省部级自然科学基金项目，曾被选为辽宁省百千万人才工程百人层次人选并享受政府特殊津贴。