报告题目: A Kruskal--Katona-type theorem for linear spaces

报 告 人：王军 教授 (上海师范大学)

时    间：2020年6月11日 下午 15:00-16:00

地    点：腾讯会议614643345

报告人简介：

王军现任上海师范大学教授、博导，曾任中国数学会组合与图论专业委员会副主任（2006-2018）。主要的研究领域是“组合数学”， 包括组合分析、组合计数、有限集和有限偏序集上的组合、字上的组合等。曾多次参加或主持国家自然科学基金项目和省部级项目。曾被选为辽宁省中青年学科带头人、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。

报告内容：

Roughly speaking, the “Kruskal-Katona-type problem for a graph G”concerned here is to describe each subset of vertices  of G that has minimal neighborhood respect to its size. We establish  a Kruskal-Katona-type theorem for the q-Kneser graph,whose vertex set consists of all k-dimensional subspaces of an n-dimensional linear space over a q-element field, two subspaces are adjacent if they have the trivial intersection. It includes as a special case the Erdos--Ko--Rado theorem for intersecting families in finite vector spaces and yields a  short proof of the Hilton-Milner theorem for nontrivial intersecting families in finite vector spaces