Abstract
A new infinite family of partial geometries with parameters s=32n-1, t== (34n-1), α== (32n-1) is constructed in the Hermitian graphs H(32n) for n≥ 1. For each geometry we describe its automorphisms and various substructures such as spreads, packings and subgeometries. A derivation process based on Baer nets in the associated affine planes is shown to yield a large number of non-isomorphic geometries from each member of the family. For n=1 we exhibit some of these derived geometries.
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Mathon, R. A New Family of Partial Geometries. Geometriae Dedicata 73, 11–19 (1998). https://doi.org/10.1023/A:1005061316760
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DOI: https://doi.org/10.1023/A:1005061316760