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DTSTART;TZID=Asia/Seoul:20210126T043000
DTEND;TZID=Asia/Seoul:20210126T173000
DTSTAMP:20260419T131818
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SUMMARY:Tuan Tran\, Minimum saturated families of sets
DESCRIPTION:A family $\mathcal F$ of subsets of [n] is called s-saturated if it contains no s pairwise disjoint sets\, and moreover\, no set can be added to $\mathcal F$ while preserving this property. More than 40 years ago\, Erdős and Kleitman conjectured that an s-saturated family of subsets of [n] has size at least $(1 – 2^{-(s-1)})2^n$. It is a simple exercise to show that every s-saturated family has size at least $2^{n-1}$\, but\, as was mentioned by Frankl and Tokushige\, even obtaining a slightly better bound of $(1/2 + \varepsilon)2^n$\, for some fixed $\varepsilon > 0$\, seems difficult. We prove such a result\, showing that every s-saturated family of subsets of [n] has size at least $(1 – 1/s)2^n$. In this talk\,  I will present two short proofs. This is joint work with M. Bucic\, S. Letzter and B. Sudakov.
URL:https://dimag.ibs.re.kr/event/2021-01-26/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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