MSC: | 05D05 | Extremal set theory |
Abstract:
$R(n,k)$ denotes the minimum possible size of a completely separating system $\bigc$ on $[n]$ with $|A|=k$ for each $A \in \bigc$. Values of $R(n,k)$ are determined for
$\binom{k-1}{2}\leq n < \binom{k}{2}$ or
$11 \leq n \leq 12$. Using the dual interpretation of completely separating systems as antichains, this paper provides corresponding results for dual $k$-regular antichains.