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# Adam Zsolt Wagner, The largest projective cube-free subsets of $Z_{2^n}$

## January 20 Monday @ 4:30 PM - 5:30 PM KST

Room B232, IBS (기초과학연구원)

### Speaker

What is the largest subset of $Z_{2^n}$ that doesn’t contain a projective d-cube? In the Boolean lattice, Sperner’s, Erdos’s, Kleitman’s and Samotij’s theorems state that families that do not contain many chains must have a very specific layered structure. We show that if instead of $Z_2^n$ we work in $Z_{2^n}$, analogous statements hold if one replaces the word k-chain by projective cube of dimension $2^{k-1}$. The largest d-cube-free subset of $Z_{2^n}$, if d is not a power of two, exhibits a much more interesting behaviour.

This is joint work with Jason Long.

## Details

Date:
January 20 Monday
Time:
4:30 PM - 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