Summary
Let I n be the lattice of intervals in the Boolean lattice I n .For I, I ⊂ I n the pair of clouds (I, I) is cross-disjoint, if I ∩ I = ø for I ∈ I, I ∈ I. We prove that for such pairs |I||I|≤32n−2 and that this bound is best possible.
Optimal pairs are up to obvious isomorphisms unique. The proof is based on a new bound on cross intersecting families in I n with a weight distribution. It implies also an Intersection Theorem for multisets of Erdös and Schönheim [91].
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© 1997 Springer-Verlag Berlin Heidelberg
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Ahlswede, R., Cai, N. (1997). Cross-Disjoint Pairs of Clouds in the Interval Lattice. In: Graham, R.L., Nešetřil, J. (eds) The Mathematics of Paul Erdös I. Algorithms and Combinatorics, vol 13. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60408-9_13
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DOI: https://doi.org/10.1007/978-3-642-60408-9_13
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