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An existence theory for pairwise balanced designs. I: Composition theorems and morphisms. (English) Zbl 0263.05014


MSC:

05B05 Combinatorial aspects of block designs
05B30 Other designs, configurations
Full Text: DOI

References:

[1] Bose, R. C.; Shrikhande, S. S., On the composition of balanced incomplete block designs, Canad. J. Math., 12, 177-188 (1960) · Zbl 0093.31906
[2] Bose, R. C.; Shrikhande, S. S., On the construction of sets of mutually orthogonal Latin squares and the falsity of a conjecture of Euler, Trans. Amer. Math. Soc., 95, 191-209 (1960) · Zbl 0093.31904
[3] Bose, R. C.; Shrikhande, S. S.; Parker, E. T., Further results on the construction of mutually orthogonal Latin squares and the falsity of a conjecture of Euler, Canad. J. Math., 12, 189-203 (1960) · Zbl 0093.31905
[4] Chowla, S.; Erdös, P.; Straus, E. G., On the maximal number of pairwise orthogonal Latin squares of a given order, Canad. J. Math., 12, 204-208 (1960) · Zbl 0093.32001
[5] Crapo, H. H.; Rota, G. C., On the foundations of combinatorial theory: combinatorial geometries, (Combinatorics. Combinatorics, Amer. Math. Soc. Proc. Symp. Pure Math., 19 (1971)) · Zbl 0216.02101
[6] Hall, M., Combinatorial Theory (1960), Blaisdell: Blaisdell Waltham, Mass
[7] Hanani, H., The existence and construction of balanced incomplete block designs, Ann. Math. Statist., 32, 361-386 (1961) · Zbl 0107.36102
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[9] Hanani, H., On the number of orthogonal Latin squares, J. Combinatorial Theory, 8, 247-271 (1970) · Zbl 0214.02902
[10] Hanani, H., On balanced incomplete block designs and related designs (1968), Israel Institute of Technology: Israel Institute of Technology Haifa, unpublished manuscript, Technion
[11] Moore, E. H., Concerning triple systems, Math. Ann., 43, 258-271 (1893) · JFM 25.0198.02
[12] Ray-Chaudhuri, D. K.; Wilson, R. M., Solution of Kirkman’s schoolgirl problem, (Combinatorics. Combinatorics, Amer. Math. Soc. Proc. Symp. Pure Math., 19 (1971)) · Zbl 0248.05009
[13] Wilson, R. M., An Existence Theory for Pairwise Balanced Designs, (Ph.D. dissertation (1969), Department of Mathematics, The Ohio State University) · Zbl 0312.05010
[14] Wilson, R. M., Cyclotomy and difference families in elementary Abelian groups, J. Number Theory, 4, 17-47 (1972) · Zbl 0259.05011
[15] Wilson, R. M., An existence theory for pairwise balanced designs. II. The structure of PBD-closed sets and the existence conjectures, J. Combinatorial Theory, 13, 246-273 (1972) · Zbl 0263.05015
[16] Bose, R. C., On the application of finite projective geometry for deriving a certain series of balanced Kirkman arrangements, Calcutta Math. Soc. Golden Jubilee, 341-354 (1959), Vol. · Zbl 0116.11202
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