A characterisation of spreads ovally-derived from Desarguesian spreads

COMBINATORICA ◽  
1994 ◽  
Vol 14 (1) ◽  
pp. 51-61 ◽  
Author(s):  
V. Jha ◽  
N. L. Johnson
Keyword(s):  
Desarguesian Spreads

Desarguesian spreads

2010 ◽  
Vol 60 (1) ◽  
pp. 15-37 ◽  
Author(s):  
Laura Bader ◽  
Guglielmo Lunardon
Keyword(s):  
Desarguesian Spreads

scholarly journals Linear sets from projection of Desarguesian spreads

2021 ◽  
Vol 71 ◽  
pp. 101798
Author(s):  
Vito Napolitano ◽  
Olga Polverino ◽  
Giovanni Zini ◽  
Ferdinando Zullo
Keyword(s):  
Linear Sets ◽  
Desarguesian Spreads

scholarly journals A geometric characterisation of Desarguesian spreads

2017 ◽  
Vol 46 (2) ◽  
pp. 455-474 ◽  
Author(s):  
Sara Rottey ◽  
John Sheekey
Keyword(s):  
Desarguesian Spreads

scholarly journals Characterisations of Elementary Pseudo-Caps and Good Eggs

10.37236/4913 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Sara Rottey ◽  
Geertrui Van de Voorde
Keyword(s):  
Geometric Proof ◽  
Similar Statement ◽  
Combinatorial Argument ◽  
Good Element ◽  
Generalised Quadrangle ◽  
Desarguesian Spreads

In this note, we use the theory of Desarguesian spreads to investigate good eggs. Thas showed that an egg in $PG(4n-1,q)$, $q$ odd, with two good elements is elementary. By a short combinatorial argument, we show that a similar statement holds for large pseudo-caps, in odd and even characteristic. As a corollary, this improves and extends the result of Thas, Thas and Van Maldeghem (2006) where one needs at least $4$ good elements of an egg in even characteristic to obtain the same conclusion. We rephrase this corollary to obtain a characterisation of the generalised quadrangle $T_3(O)$ of Tits. Lavrauw (2005) characterises elementary eggs in odd characteristic as those good eggs containing a space that contains at least $5$ elements of the egg, but not the good element. We provide an adaptation of this characterisation for weak eggs in odd and even characteristic. As a corollary, we obtain a direct geometric proof for the theorem of Lavrauw.

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