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Support sizes of threefold resolvable triple systems

✍ Scribed by Yanxun Chang; Giovanni Lo Faro; Hao Shen

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 144 KB
Volume: 11
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.10037

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✦ Synopsis

Abstract

Let SS~R~(v, 3) denote the set of all integer b* such that there exists a RTS(v, 3) with b* distinct triples. In this paper, we determine the set SS~R~(v, 3) for v ≡ 3 (mod 6) and v ≥ 3 with only five undecided cases. We establish that SS~R~(v, 3) = P(v, 3) for v ≡ 3 (mod 6), v ≥ 21 and v ≠ 33, 39 where P(v, 3) = {m~v~, m~v~ + 4, m~v~ + 6, m~v~ + 7, …, 3__m__~v~} and m~v~, = v(v − 1)/6. As a by‐product, we remove the last two undecided cases for the intersection numbers of Kirkman triple system of order 27, this improves the known result provided in [2]. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 275–289, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10037

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