Martin Grüttmüller

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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)
In this paper, we investigate the PBD-closure of sets K with In particular, we show that v ≡ 1 mod 6, v ≥ 98689 implies v ∈ B({7, 13}). As a preliminary result , many new 13-GDDs of type 13 q and resolvable BIBD with block size 6 or 12 are also constructed. Furthermore, we show some elements to be not essential in a Wilson bases for the PBD-closed set {v :(More)