Completely separating systems of k-sets

Completely separating systems of k-sets

Dickson On a problem concerning separating systems of a nite set, Journal of Combinatorial Theory, 7 (1969), 191{196.] introduced the notion of a completely separating set system. We study such systems with the additional constraint that each set in the system has the same size. Let T denote an n-set. We say that a subset S of T separates i from j if i 2 S and j 6 2 S. A collection of k-sets C ...

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

Minimal completely separating systems of sets

Let [n] denote an n-set. A subset,) of [n] i from j if i and j t/:. 5'. A collection of k-sets n called (n, k) completely if, for each ordered pair j) E [n] x [71,] with i n which i from j. Let denote the size of a smallest (71" k) completely Amongst other things, it will be shown that R( 71" k) for n > except when n (Hl) 1, and R(71" k) k + 1 for G) n k 2 /2. These results build on and extend ...

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.

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