Excluded subposets in the Boolean lattice

Gyula O.H. Katona
2005 Discrete Mathematics & Theoretical Computer Science  
International audience We are looking for the maximum number of subsets of an n-element set not containing 4 distinct subsets satisfying $A ⊂B, C ⊂B, C ⊂D$. It is proved that this number is at least the number of the $\lfloor \frac{n }{ 2}\rfloor$ -element sets times $1+\frac{2}{ n}$, on the other hand an upper bound is given with 4 replaced by the value 2.
doi:10.46298/dmtcs.3409 fatcat:4pbj3wxejbhblbznobt6qbdfxe