### Excluded subposets in the Boolean lattice

*Gyula O.H. Katona*

#### Abstract

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 ⌊n / 2⌋-element sets times 1+2 / n, on the other hand an upper bound is given with 4 replaced by the value 2.

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