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Support Sizes of Threefold Resolvable Triple Systems by Yanxun Chang; Giovanni Lo Faro; Hao Shen is a Engineering article available to read on EtoBox.

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## 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

Who reads Support Sizes of Threefold Resolvable Triple Systems?

Author

Yanxun Chang; Giovanni Lo Faro; Hao Shen

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); John Wiley & Sons Inc.; Wiley (ISSN 1063-8539)

Published

2003

Language

EN

Field

Engineering (Physical Sciences)