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Translation planes constructed by multiple hyper-regulus replacement
Authors:Vikram Jha  Norman L Johnson
Institution:1. Mathematics Department, Glasgow Caledonian University, Cowcaddens Road, Glasgow, G4 OBA, Scotland, UK
2. Mathematics Department, University of Iowa, Iowa City, IA, 52242, USA
Abstract:New classes of mutually disjoint hyper-reguli of order q n , for n > 2, are determined, which are not André hyper-reguli if n > 3. If n is odd, each hyper-regulus permits at least two replacements and if q is odd and (n, q?1) = 1, there are (q?1)/2 mutually disjoint hyper-reguli each of which may be replaced at least two ways. Each of the possible 2(q-1)/2 translation planes constructed is not André or generalized André. There are also new constructions of mixed subgeometry partitions.
Keywords:
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