✍ Scribed by L. Ji
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A (2,3)‐packing on X is a pair (X,$\cal A$), where $\cal A$ is a set of 3‐subsets (called blocks) of X, such that any pair of distinct points from X occurs together in at most one block. Its leave is a graph (X,E) such that E consists of all the pairs which do not appear in any block of $\cal A$. In this article, we shall construct a set of 6__k__ − 2 disjoint (2,3)‐packings of order 6__k__ + 4 with K~1,3~ ∪ 3__kK__~2~ or G~1~ ∪ (3__k__ − 1)K~2~ as their common leave for any integer k ≥ 1 with a few possible exceptions (G~1~ is a special graph of order 6). Such a system can be used to construct perfect threshold schemes as noted by Schellenberg and Stinson (1989). © 2006 Wiley Periodicals, Inc. J Combin Designs
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Single Crystals of [K 3 (O 3 SCF 3 ) 3 (O 2 C 4 H 6 ) 2 ] (1) have been obtained as a by-product from the reaction of KNPPh 3 with Yb(O 3 SCF 3 ) 3 in THF with subsequent addition of butyrolactone. The structure of 1 consists of three symmetry-independent potassium ions which are linked by the oxyge