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Counting arcs in projective planes via Glynn’s algorithm
An n -arc in a projective plane is a collection of n distinct points in the plane, no three of which lie on a line. Formulas counting the number of n -a...
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New Non-existence Proofs for Ovoids of Hermitian Polar Spaces and Hyperbolic Quadrics
We provide new proofs for the non-existence of ovoids in hyperbolic spaces of rank at least four in even characteristic, and for the Hermitian polar...
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Oriented Steiner loops
We study oriented Steiner loops L which are strictly related to oriented Steiner triple systems and discuss thoroughly the interplay between the...
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The Geometry of Elation Groups of a Finite Projective Space
We study the geometry of point-orbits of elation groups with a given center and axis of a finite projective space. We show that there exists a 1-1...
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The Doubly-Transitive Focal-Spreads
A focal-spread of order q t and type ( t , k ), t > k is a partition of a vector space of dimension t + k over GF ( q ) by a one subspace of dimension t ,...
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Fano subplanes in finite Figueroa planes
It has been conjectured that all non-desarguesian projective planes contain a Fano subplane. The Figueroa planes are a family of non-translation...
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Small point sets of PG(n, p 3h ) intersecting each line in 1 mod p h points
The main result of this paper is that point sets of PG( n , q ), q = p 3 h , p ≥ 7 prime, of size < 3( q n -1 + 1)/2 intersecting each line in 1 modulo
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On the intersection of Hermitian surfaces
We provide a description of the configuration arising from intersection of two Hermitian surfaces in PG(3, q ), provided that the linear system they...
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On the matricial version of Fermat–Euler congruences
The congruences modulo the primary numbers n = p a are studied for the traces of the matrices A n and A n -φ( n ) , where A is an integer matrix and φ( n )...
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A Minimal Triangulation of the Hopf Map and its Application
We give a minimal triangulation η: S
12 3 → S4 2 of the Hopf map h : S 3 → S 2 and use it to obtain a new construction of the 9-vertex complex... -
Characterisations of Flock Quadrangles
We characterise the Hermitian and Kantor flock generalized quadrangles of order ( q 2 , q ), q even, (associated with the linear and Fisher–Thas–Walker...
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Some Codes Determined by Their Weight Enumerators
Knowing the weight enumerator of a linear code allows us to have much information about the code; its dimension, length, minimum distance, the sum of...
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Normal Spreads
In Dedicata 16 (1984), pp. 291–313, the representation of Desarguesian spreads of the projective space PG(2 t − 1, q ) into the Grassmannian of the...
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On infinite K-clan geometry
We discuss infinite elation generalized quadrangles as group coset geometries and use this approach to deal with the special case of those associated...
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Flocks, Ovoids of Q(4,q)and Designs
We prove that an ovoid O of Q(4,q),q odd, is the Thas' ovoid associated with a semifield flock if and only if O represents, on the Klein quadric, a...