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Holey Steiner pentagon systems

✍ Scribed by R. J. R. Abel; F. E. Bennett; H. Zhang

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 214 KB
Volume: 7
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1999)7:1<41::aid-jcd6>3.0.co;2-q

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✦ Synopsis

In this article, it is shown that the necessary conditions for the existence of a holey Steiner pentagon system (HSPS) of type h n are also sufficient, except possibly for the following cases: (1) when n = 15, and h ≡ 1 or 5 (mod 6) where h ≡ 0 (mod 5), or h = 9; and (2) (h, n) ∈ {(6, 6), (6, 36), (15, 19), (15, 23), (15, 27), (30, 18), (30, 22), (30, 24)}. Moreover, the results of this article guarantee the analogous existence results for group divisible designs (GDDs) of type h n with block-size k = 5 and index λ = 2.

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