Completely separating systems of k-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.

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 ...

Using a Data Mining Tool and FP-Growth Algorithm Application for Extraction of the Rules in two Different Dataset (TECHNICAL NOTE)

In this paper, we want to improve association rules in order to be used in recommenders. Recommender systems present a method to create the personalized offers. One of the most important types of recommender systems is the collaborative filtering that deals with data mining in user information and offering them the appropriate item. Among the data mining methods, finding frequent item sets and ...