论文信息 - Resolvable perfect Mendelsohn designs with block size five

Resolvable perfect Mendelsohn designs with block size five

A necessary condition for the existence of a resolvable (v, 5, 1 )-perfect Mendelsohn design is v ≡ 0 (mod 5). This condition is shown to be sufficient for v ≥ 215, with two known exceptions plus at most 17 possible exceptions below this value.

[1] Frank E. Bennett,et al. Existence of HPMDs with block size five , 1997 .

[2] N. S. Mendelsohn. Perfect cyclic designs , 1977, Discret. Math..

[3] D. F. Hsu,et al. GENERALIZED COMPLETE MAPPINGS, NEOFIELDS, SEQUENCEABLE GROUPS AND BLOCK DESIGNS. II , 1984 .

[4] Frank E. Bennett,et al. Resolvable Perfect Cyclic Designs , 1980, J. Comb. Theory, Ser. A.

[5] Anne Germa,et al. Resolvable Decomposition of Kn , 1979, J. Comb. Theory, Ser. A.

[6] P. Östergård,et al. There exists no (15,5,4) RBIBD † * , 2001 .

[7] Richard M. Wilson,et al. Constructions and Uses of Pairwise Balanced Designs , 1975 .

[8] R. Julian R. Abel,et al. Resolvable balanced incomplete block designs with block size 5 , 2001 .

[9] Hanfried Lenz,et al. Design theory , 1985 .

[10] Zhang Xuebin. On the existence of (v, 4, 1)-RPMD , 1996, Ars Comb..

[11] R. Julian R. Abel,et al. Some new RBIBDs with block size 5 and PBDs with block sizes ≡1 mod 5 , 1997, Australas. J Comb..

[12] Douglas R. Stinson,et al. Frames with Block Size Four , 1992, Canadian Journal of Mathematics.

[13] Frank E. Bennett,et al. Resolvable Mendelsohn triple systems with equal sized holes , 1997 .