Let S be a proper partial geometry pg(s, t, 2), and let G be an abelian group of automorphisms of S acting regularly on the points of S. Then either t ≡ 2 (mod s+1) or S is a pg(5, 5, 2) isomorphic to the partial geometry of van Lint and Schrijver . This result is a new step towards the classification of partial geometries with an abelian Singer group… (More)
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 overview what is known about partial ovoids and spreads of finite (classical) generalized quadrangles. In the first, respectively the second , part of the paper we will be mostly concerned with small, respectively large, maximal partial ovoids and spreads. Also connections with other interesting objects in finite geometry will be explained.… (More)
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),… (More)
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.
In  De Clerck, De Winter and Maes counted the number of non-isomorphic Mathon maximal arcs of degree 8 in PG(2, 2 h), h = 7 and prime. In this article we will show that in PG(2, 2 7) a special class of Mathon maximal arcs of degree 8 arises which admits a Singer group (i.e. a sharply transitive group) on the 7 conics of these arcs. We will give a… (More)
Quantitative analysis on intracoronary optical coherence tomography (OCT) image data (e.g. QOCT) is currently performed by a time-consuming manual contour tracing process in many individual OCT images acquired during a pullback procedure (frame-based method). In order to get a more efficient quantitative analysis process and to investigate the possibilities… (More)