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