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Journals and Conferences
In this note we characterize thick finite generalized quadrangles constructed from a generalized hyperoval as those admitting an abelian Singer group, i.e., an abelian group acting regularly on the points.
Let Π = (P,L, I) denote a rank two geometry. In this paper, we are interested in the largest value of |X||Y | where X ⊂ P and Y ⊂ L are sets such that (X×Y )∩I = ∅. Let α(Π) denote this value. We concentrate on the case where P is the point set of PG(n, q) and L is the set of k-spaces in PG(n, q). In the case that Π is the projective plane PG(2, q), Haemers… (More)
In this article, we prove that amongst all n by n bipartite graphs of girth at least six, where n = q + q + 1 ≥ 157, the incidence graph of a projective plane of order q, when it exists, has the maximum number of cycles of length eight. This characterizes projective planes as the partial planes with the maximum number of quadrilaterals.
We present results on the size of the smallest maximal partial ovoids and on the size of the smallest maximal partial spreads of the generalized quadrangles W (q) and Q(4, q).
In 1969, Denniston gave a construction of maximal arcs of degree d in Desarguesian projective planes of even order q, for all d dividing q. In 2002 Mathon gave a construction method generalizing the one of Denniston. We will give a new geometric approach to these maximal arcs. This will allow us to count the number of non-isomorphic Mathon maximal arcs of… (More)
In this paper we introduce semi-pseudo-ovoids, as generalizations of the semi-ovals and semi-ovoids. Examples of these objects are particular classes of SPG-reguli and some classes of m-systems of polar spaces. As an application it is proved that the axioms of pseudo-ovoid O(n, 2n, q) in PG(4n − 1, q) can be considerably weakened and further a useful and… (More)
All known finite generalized quadrangles that admit an automorphism group acting sharply transitively on their point set arise by Payne derivation from thick elation generalized quadrangles of order s with a regular point. In these examples only two groups occur: elementary abelian groups of even order and odd order Heisenberg groups of dimension 3. In … (More)