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On the covering of t-sets with (t + 1)-sets:C(9, 5, 4) and C(10, 6, 5)

✍ Scribed by D. de Caen; D.L. Kreher; S.P. Radziszowski; W.H. Mills

Book ID: 103057614
Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 1003 KB
Volume: 92
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90267-6

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✦ Synopsis

On the covering of I-sets with (t + I)-sets: C(9,5,4) and C(10,6,.5), Discrete Mathematics 92 (1991) 65-77.

A (v, k, t) covering system is a pair (X, S) where X is a tr-set of points and D is a family of k-subsets. called blocks, of X such that every t-subset of X is contained in p least one block. The minimum possible number of blocks in a (v, k, t) covering system is denoted by C(v, k, I). It is proven that there are exactly three non-isomorphic systems giving C(9,5,4) = 30, and a unique system giving C( 10, 6,5) = 50.

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