Pairwise balanced designs whose block size set contains seven and thirteen |
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| Authors: | M. Greig M. Grüttmüller S. Hartmann |
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| Affiliation: | 1. Greig Consulting, North Vancouver, B.C., Canada V7L 4R3;2. Department of Mathematics, University of Rostock, 18051 Rostock, Germany;3. Department of Information Systems, Massey University, Private Bag 11222, Palmerston North, New Zealand |
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| Abstract: | In this paper, we investigate the PBD‐closure of sets K with {7,13} ? K ? {7,13,19,25,31,37,43}. In particular, we show that ν ≡ 1 mod 6, ν ≥ 98689 implies ν ? B({7,13}). As an intermediate result, many new 13‐GDDs of type 13q and resolvable BIBD with block size 6 or 12 are also constructed. Furthermore, we show some elements to be not essential in a Wilson basis for the PBD‐closed set {ν: ν ≡ 1 mod 6, ν ≥ 7}. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 283–314, 2007 |
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| Keywords: | pairwise balanced design group divisible design Wilson basis resolvable design |
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