论文信息 - Multiplicative Designs I: The Normal and Reducible Cases

Multiplicative Designs I: The Normal and Reducible Cases

Abstract Multiplicative designs, square designs with a rank one intersection pattern, are investigated. In particular we determine all designs for which some incidence matrix is reducible and we show if some incidence matrix is normal the design must be uniform with three families of exceptions. Some new designs are constructed.

W. G. Bridges | R. A. Mena | W. Bridges | R. Mena

[1] W. G. Bridges,et al. Some results on ?-designs , 1970 .

[2] de Ng Dick Bruijn. A combinatorial problem , 1946 .

[3] H. Ryser,et al. An extension of a theorem of de Bruijn and Erdös on combinatorial designs , 1968 .

[4] Robert Patenaude,et al. The lambda-Designs with Multiplicative Duals , 1974, J. Comb. Theory, Ser. A.

[5] Kulendra N. Majumdar. On some Theorems in Combinatorics Relating to Incomplete Block Designs , 1953 .

[6] George Szekeres,et al. On a combinatorial generalization of 27 lines associated with a cubic surface , 1969, Journal of the Australian Mathematical Society.

[7] H. J. Ryser. Symmetric Designs and Related Configurations , 1972, J. Comb. Theory, Ser. A.

[8] Earl S. Kramer,et al. The determination of all λ-designs with λ=3 , 1970 .

[9] W. G. Bridges. Replication results for certain combinatorial configurations , 1973, Discret. Math..

[10] W. G. Bridges. On the replications of certain multiplicative designs , 1972 .

[11] Earl S. Kramer,et al. On λ-designs , 1974 .

[12] Douglas R. Woodall. Square λ-Linked Designs , 1970 .