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Doubly Resolvable Nearly Kirkman Triple Systems |
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| Authors: | R Julian R Abel Nigel Chan Charles J Colbourn E R Lamken Chengmin Wang Jinhua Wang |
| Institution: | 1. School of Mathematics and Statistics, University of New South Wales N.S.W. 2052, , Australia;2. School of Computing, Informatics, and Decision Engineering, Arizona State University, , Tempe, Arizona 85287–8809;3. Mathematical Sciences Research Institute, , California 94720–5020;4. School of Science, Jiangnan University, , Wuxi 214122, P.R. China;5. School of Sciences, Nantong University, , Nantong 226007, P.R. China |
| Abstract: | Necessary conditions for existence of a resolvable group divisible design (GDD) with block size 3 and type  (a nearly Kirkman triple system, NKTS(v)), are  and  (mod 6). In this paper, we look at doubly resolvable NKTS(v)s; here we find that these necessary conditions are sufficient, except possibly for 64 values of v. |
| Keywords: | nearly Kirkman triple system doubly resolvable Kirkman square frame AMS subject classification: 05B07 |