A Ramsey-Sperner theorem |
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Authors: | Z Füredi |
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Institution: | (1) Mathematical Institute of the Hungarian Academy of Science, P.O.B. 127, H-1364 Budapest, Hungary |
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Abstract: | Letn≥k≥1 be integers and letf(n, k) be the smallest integer for which the following holds: If ℱ is a family of subsets of ann-setX with |ℱ|<f(n,k) then for everyk-coloring ofX there existA
B ∈ ℱ,A∈B, A⊂B such thatB-A is monochromatic. Here it is proven that for a fixedk there exist constantsc
k
andd
k
such that
and
ask→∞. The proofs of both the lower and the upper bounds use probabilistic methods. |
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Keywords: | |
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