报告人：王军 （上海师范大学 教授）
报告时间：2024年10月13日(星期日)15:00
报告地点：理学院442报告厅
联系人：组合图论研究团队
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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.
报告人简介：王军，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国务院政府特殊津贴。
理学院
2024年10月10日
