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Saturating Sperner Families |
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| Authors: | Dániel Gerbner Balázs Keszegh Nathan Lemons Cory Palmer Dömötör Pálvölgyi Balázs Patkós |
| Institution: | 1. Hungarian Academy of Sciences, Alfréd Rényi Institute of Mathematics, P.O.B. 127, Budapest, 1364, Hungary 3. Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA 4. University of Illinois, Urbana-Champaign, Urbana, IL, 61801, USA 2. Department of Computer Science, E?tv?s Loránd University, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary |
| Abstract: | A family ${\mathcal{F} \subseteq 2^{n]}}$ saturates the monotone decreasing property ${\mathcal{P}}$ if ${\mathcal{F}}$ satisfies ${\mathcal{P}}$ and one cannot add any set to ${\mathcal{F}}$ such that property ${\mathcal{P}}$ is still satisfied by the resulting family. We address the problem of finding the minimum size of a family saturating the k-Sperner property and the minimum size of a family that saturates the Sperner property and that consists only of l-sets and (l + 1)-sets. |
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