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# Tuan Tran, Minimum saturated families of sets

## January 26 Tuesday @ 4:30 AM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

### Speaker

Tuan Tran
IBS Discrete Mathematics Group
https://tuaentran.wixsite.com/homepage

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.

## Details

Date:
January 26 Tuesday
Time:
4:30 AM - 5:30 PM KST
Event Category:
Event Tags:

Room B232
IBS (기초과학연구원)

## Organizer

Sang-il Oum (엄상일)
Website:
https://dimag.ibs.re.kr/home/sangil/
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209