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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)

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.