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Tight bound for Katona intersecting shadow theorem

刘西之(University of Illinois at Chicago)
Tuesday, July 14th, 2020, 8:00 PM  腾讯会议:235 207 220
 
主持人:袁龙图
报告时间:7月14日20:00-21:00
报告平台:腾讯会议:235 207 220

报告人介绍:刘西之现为伊利诺伊大学芝加哥分校的博士研究生,研究方向为极值组合与超图。

报告内容摘要:A fundamental result in extremal set theory is Katona's intersecting shadow theorem, which extends the Kruskal-Katona theorem by giving a lower bound on the size of the shadow of an intersecting family of k-sets in terms of its size. We improve this classical result and a related result of Ahlswede, Aydinian, and Khachatrian by proving tight bounds for families that can be quite small.

Katona's theorem was extended by Frankl to families with matching number s. We improve Frankl's result by giving tight bounds for large n.

This is joint work with Dhruv Mubayi.
   
 
 
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