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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
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[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
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[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, () · Zbl 0248.05009
[13] Wilson, R.M, An existence theory for pairwise balanced designs, () · 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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