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We study maximal families A of subsets of [n] = {1, 2,. .. , n} such that A contains only pairs and triples and A ⊆ B for all {A, B} ⊆ A, i.e. A is an antichain. For any n, all such families A of minimum size are determined. This is equivalent to finding all graphs G = (V, E) with |V | = n and with the property that every edge is contained in some triangle… (More)

This paper deals with completion of partial latin squares L = (l ij) of order n with k cyclically generated diagonals (l i+t,j+t = l ij + t if l ij is not empty; with calculations modulo n). There is special emphasis on cyclic completion. Here, we present results for k = 2,. .. , 7 and odd n ≤ 21, and we describe the computational method used… (More)

We describe a method used to prove nonexistence of pairwise balanced designs. We determine the exact closure of all subsets K of the set f3; 4

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