More results on perfect (3,3,6k + 4; 6k − 2)‐threshold schemes |
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Authors: | L Ji |
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Institution: | Department of Mathematics, Suzhou University, Suzhou 215006, China |
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Abstract: | A (2,3)‐packing on X is a pair (X, ), where 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 . In this article, we shall construct a set of 6k ? 2 disjoint (2,3)‐packings of order 6k + 4 with K1,3 ∪ 3kK2 or G1 ∪ (3k ? 1)K2 as their common leave for any integer k ≥ 1 with a few possible exceptions (G1 is a special graph of order 6). Such a system can be used to construct perfect threshold schemes as noted by Schellenberg and Stinson ( 22 ). © 2006 Wiley Periodicals, Inc. J Combin Designs |
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Keywords: | large set group divisible t‐design t‐wise balanced design s‐fan design threshold scheme |
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