P3BD-closed sets
Copyright policy )P3BD-closed sets
Summary: A concept called P3BD-closed set is introduced to describe a set of positive integers which is both PBD-closed and 3BD-closed. The theory of P3BD-closure is developed and a few examples of P3BD-closed sets are exhibited. In the process, the existence spectrum of OLIQ \(^{\diamond }\)s (overlarge sets of idempotent quasigroups with their own idempotent orthogonal mates) is almost determined. A pair of orthogonal OLIQ \(^{\diamond }\)s is shown to asymptotically exist. The existence of OLIQ s (overlarge sets of idempotent quasigroups with their own orthogonal mates not necessarily specifying idempotency) is also established with only 10 possible exceptions remained.
- Beijing Jiaotong University China (People's Republic of)
orthogonal, P3BD-closed set, idempotent quasigroup, overlarge set, Orthogonal arrays, Latin squares, Room squares, t-wise balanced design, Combinatorial aspects of block designs
orthogonal, P3BD-closed set, idempotent quasigroup, overlarge set, Orthogonal arrays, Latin squares, Room squares, t-wise balanced design, Combinatorial aspects of block designs
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