报告题目：Kruskal-Katona Theorems，maximal intersecting families and cross-intersecting families

主 讲 人： 王军 教授

报告时间： 2024年8月19日 周一下午15:00-17:00

报告地点： 数理楼224

报告摘要：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 report 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 the following conditions: (i) they are arbitrary; (ii) They have different sizes; (iii) neither of them is; (iv) They have different sizes and not trivial.

个人简介：上海师范大学数理学院教授（二级）， 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，近年来工作重点在有限集上的组合，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。