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Kirkman school project designs. (English) Zbl 0929.05013

A Kirkman school project (KSP) design on \(v\) elements consists of the maximum admissible number of disjoint parallel classes each containing blocks of size three except possibly one of size two or four. The existence problem for KSP designs with \(v \equiv 0,2\) (mod 3) was settled by A. Černý, P. Horák and W. D. Wallis [Discrete Math. 167/168, 189-196 (1997; Zbl 0873.05015)]. In the paper under review, the authors completely resolve the existence problem for \(v \equiv 4\) (mod 3) and nearly completely cover the case \(v \equiv 1\) (mod 3).

MSC:

05B30 Other designs, configurations
05B05 Combinatorial aspects of block designs

Citations:

Zbl 0873.05015
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References:

[1] R.J.R. Abel, A.E. Brouwer, C.J. Colbourn, J.H. Dinitz, Mutually orthogonal latin squares (MOLS), in: C.J. Colbourn, J.H. Dinitz (Eds.), CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton FL, 1996, pp. 111-142.; R.J.R. Abel, A.E. Brouwer, C.J. Colbourn, J.H. Dinitz, Mutually orthogonal latin squares (MOLS), in: C.J. Colbourn, J.H. Dinitz (Eds.), CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton FL, 1996, pp. 111-142.
[2] T. Beth, D. Jungnickel, H. Lenz, Design Theory, Cambridge University Press, Cambridge, 1986.; T. Beth, D. Jungnickel, H. Lenz, Design Theory, Cambridge University Press, Cambridge, 1986.
[3] Brickell, E. F., A few results in message authentication, Congr. Numer., 43, 141-154 (1984) · Zbl 0561.05042
[4] Černý, A.; Horák, P.; Wallis, W. D., Kirkman’s school projects, Discrete Math., 167/168, 189-196 (1997) · Zbl 0873.05015
[5] J.H. Dinitz, D.R. Stinson, Room squares and related designs, in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory, Wiley, New York, 1992, 137-204.; J.H. Dinitz, D.R. Stinson, Room squares and related designs, in: J.H. Dinitz, D.R. Stinson (Eds.), Contemporary Design Theory, Wiley, New York, 1992, 137-204. · Zbl 0768.05015
[6] Furino, S. C.; Mullin, R. C., Block designs with large holes and \(α\) resolvable BIBDs, J. Combin. Des., 1, 101-112 (1993) · Zbl 0817.05006
[7] Hanani, H., Balanced incomplete block designs and related designs, Discrete Math., 11, 255-369 (1975) · Zbl 0361.62067
[8] R.C. Mullin, H-D.O.F. Gronau, PBDs, frames, and resolvability in: C.J. Colbourn, J.H. Dinitz (Eds.), CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton FL, 1996, pp. 224-226.; R.C. Mullin, H-D.O.F. Gronau, PBDs, frames, and resolvability in: C.J. Colbourn, J.H. Dinitz (Eds.), CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton FL, 1996, pp. 224-226.
[9] Rees, R.; Stinson, D. R., Kirkman triple systems with maximum subsystems, Ars Combin., 25, 125-132 (1988) · Zbl 0679.05011
[10] Stinson, D. R., Frames for Kirkman triple systems, Discrete Math., 65, 289-300 (1987) · Zbl 0651.05015
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