2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05)
Stefan Felsner (ed.)
DMTCS Conference Volume AE (2005), pp. 229230
author:  Gyula O.H. Katona 

title:  Excluded subposets in the Boolean lattice 
keywords:  extremal problems, families of subsets 
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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reference:  Gyula O.H. Katona (2005), Excluded subposets in the Boolean lattice, in 2005 European Conference on Combinatorics, Graph Theory and Applications (EuroComb '05), Stefan Felsner (ed.), Discrete Mathematics and Theoretical Computer Science Proceedings AE, pp. 229230 
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