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 Є C with a Є A B and b Є 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 natural class of antichains.