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.
SPERNER CAPACITIES / L., Gargano; Korner, Janos; U., Vaccaro. - In: GRAPHS AND COMBINATORICS. - ISSN 0911-0119. - STAMPA. - 9:1(1993), pp. 31-46. [10.1007/bf01195325]
SPERNER CAPACITIES
KORNER, JANOS;
1993
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
