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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
报告平台:腾讯会议:235 207 220


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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