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Excluded subposets in the Boolean lattice

2005
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Discrete Mathematics & Theoretical Computer Science
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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