3 research outputs found

    Enumeration of Nonsingular Buekenhout Unitals

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    The only known enumeration of Buekenhout unitals occurs in the Desarguesian plane PG(2,q2)PG(2,q^2).  In this paper we develop general techniques for enumerating the nonsingular Buekenhoutunitals embedded in any two-dimensional translation plane, and apply these techniques to obtain such an enumeration in the regular nearfield planes, the odd-order Hall planes, and the flag-transitive affine planes.  We also provide some computer data for small-order André planes of index two and give partial results toward an enumeration in this case

    Part I:

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    Unitals and replaceable t-nests

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    Let Ū be a known unital of PG(2, q2), q odd, and let N be a t-nest in a regular spread S. Suppose we replace N by a replacement set N to form the new spread S' = (S\Ň) UŇ). Using the Bruck-Bose correspondence, we look at the afhne points of Ū in V{S) = PG(2,q 2) and see whether the corresponding afhne point set in the new plane V{S') can be completed to a unital.S.G. Barwick and D.J. Marshallhttp://ajc.maths.uq.edu.au/volume_contents.php3?vol=4
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