A New Family of Partial Geometries

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Abstract

A new infinite family of partial geometries with parameters s=32n−1, t=½(34n−1), α=½ (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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