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EnglishWe determine the asymptotics of the largest family of qualitatively 2-independent k-partitions of an n-set, for every k > 2. We generalize a Sperner-type theorem for 2-partite sets of Korner and Simonyi to the k-partite case. Both results have the feature that the corresponding trivial information-theoretic upper bound is tight. The results follow from a more general Sperner capacity theorem for a family of graphs in the sense of our previous work on Sperner theorems on directed graphs.
http://hdl.handle.net/11573/16089| Titolo: | SPERNER CAPACITIES |
| Autori interni: | KORNER, JANOS |
| Data di pubblicazione: | 1993 |
| Rivista: | GRAPHS AND COMBINATORICS |
| Abstract: | We determine the asymptotics of the largest family of qualitatively 2-independent k-partitions of an n-set, for every k > 2. We generalize a Sperner-type theorem for 2-partite sets of Korner and Simonyi to the k-partite case. Both results have the feature that the corresponding trivial information-theoretic upper bound is tight. The results follow from a more general Sperner capacity theorem for a family of graphs in the sense of our previous work on Sperner theorems on directed graphs. |
| Handle: | http://hdl.handle.net/11573/16089 |
| Appare nelle tipologie: | 01.a Pubblicazione su Rivista |
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