Maximal partial ovoids and maximal partial spreads in hermitian generalized quadrangles

2008 ◽  
Vol 16 (2) ◽  
pp. 101-116 ◽  
Author(s):  
K. Metsch ◽  
L. Storme
Keyword(s):  
Generalized Quadrangles ◽  
Partial Spreads ◽  
Partial Ovoids

scholarly journals Partial ovoids and partial spreads in hermitian polar spaces

2007 ◽  
Vol 47 (1-3) ◽  
pp. 21-34 ◽  
Author(s):  
J. De Beule ◽  
A. Klein ◽  
K. Metsch ◽  
L. Storme
Keyword(s):  
Polar Spaces ◽  
Partial Spreads ◽  
Partial Ovoids

Small maximal partial spreads in classical finite polar spaces

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Andreas Klein ◽  
Klaus Metsch ◽  
Leo Storme
Keyword(s):  
Lower Bounds ◽  
Polar Spaces ◽  
Partial Spreads ◽  
Partial Ovoids

AbstractWe prove lower bounds on the size of small maximal partial spreads inQ+(4n+ 1,q),W(2n+ 1,q), andH(2n+ 1,q2). This research on the size of smallest maximal partial spreads in classical finite polar spaces is part of a detailed study on small and large maximal partial ovoids and spreads in classical finite polar spaces, performed in [De Beule, Klein, Metsch, Storme, Des. Codes Cryptogr 47: 21–34, 2008, De Beule, Klein, Metsch, Storme, European J. Combin 29: 1280–1297, 2008].

scholarly journals On the smallest maximal partial ovoids and spreads of the generalized quadrangles W(q) and Q(4,q)

2007 ◽  
Vol 28 (7) ◽  
pp. 1934-1942 ◽  
Author(s):  
M. Cimráková ◽  
S. De Winter ◽  
V. Fack ◽  
L. Storme
Keyword(s):  
Generalized Quadrangles ◽  
Partial Ovoids

scholarly journals Partial ovoids and partial spreads in symplectic and orthogonal polar spaces

2008 ◽  
Vol 29 (5) ◽  
pp. 1280-1297 ◽  
Author(s):  
J. De Beule ◽  
A. Klein ◽  
K. Metsch ◽  
L. Storme
Keyword(s):  
Polar Spaces ◽  
Partial Spreads ◽  
Partial Ovoids

scholarly journals MOUFANG QUADRANGLES OF MIXED TYPE

2008 ◽  
Vol 50 (1) ◽  
pp. 143-161
Author(s):  
KOEN STRUYVE ◽  
HENDRIK VAN MALDEGHEM
Keyword(s):  
Mixed Type ◽  
Geometric Characterization ◽  
Weak Version ◽  
Generalized Quadrangles

AbstractIn this paper, we present some geometric characterizations of the Moufang quadrangles of mixed type, i.e., the Moufang quadrangles all the points and lines of which are regular. Roughly, we classify generalized quadrangles with enough (to be made precise) regular points and lines with the property that the dual nets associated to the regular points satisfy the Axiom of Veblen-Young, or a very weak version of the Axiom of Desargues. As an application we obtain a geometric characterization and axiomatization of the generalized inversive planes arising from the Suzuki-Tits ovoids related to a polarity in a mixed quadrangle. In the perfect case this gives rise to a characterization with one axiom less than in a previous result by the second author.

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