Minimal completely separating systems of sets

Completely separating systems of k-sets for (k-12) ≤ n < (k2) or 11 ≤ k ≤ 12

Here R(n, k) denotes the minimum possible size of a completely separating system C on [n] with |A| = k for each A ∈ C. Values of R(n, k) are determined for ( k−1 2 ) ≤ n < (k 2 ) or 11 ≤ n ≤ 12. Using the dual interpretation of completely separating systems as antichains, this paper provides corresponding results for dual k-regular antichains.

Separating Systems of k - sets for k = 11 or k = 12

R(n,k) denotes the minimum possible size of a completely separating system C on {1,2,…,n} with |A|=k for each set A of C. Values of R(n,k) are determined for k=11 or k=12 and several other results are mentioned. Using the dual interpretation of completely separating systems as antichains, it provides corresponding results for dual k-regular antichains.

Minimal (n) and (n, h, k) Completely Separating Systems

Completely separating systems of k-sets for 7 ≤ k ≤ 10

On the number of minimal completely separating systems and antichains in a Boolean lattice

An (n)completely separating system C ((n)CSS) is a collection of blocks of [n] = {1, . . . , n} such that for all distinct a, b ∈ [n] there are blocks A,B ∈ C with a ∈ A \B and b ∈ B \A. An (n)CSS is minimal if it contains the minimum possible number of blocks for a CSS on [n]. The number of non-isomorphic minimal (n)CSSs is determined for 11 ≤ n ≤ 35. This also provides an enumeration of a nat...