Using the connection between translation spreads of the generalized hexagon H(q) and linear sets (see Cardinali et al. in Eur J Comb 23:367–376, 2002; Lunardon and Polverino in J Algebraic Comb 18:255–262, 2003), the non-existence of Fq-translation spreads of H(q2) when p > 3, q = ph, and q is large enough is proven. This answers to a question posed in [Marino and Polverino in J Algebraic Comb 42:725-744, 2015].
The non-existence of F_q translation spreads of H(q^2)
Bartoli, Daniele;Giannoni, Alessandro;Giulietti, Massimo;
2025
Abstract
Using the connection between translation spreads of the generalized hexagon H(q) and linear sets (see Cardinali et al. in Eur J Comb 23:367–376, 2002; Lunardon and Polverino in J Algebraic Comb 18:255–262, 2003), the non-existence of Fq-translation spreads of H(q2) when p > 3, q = ph, and q is large enough is proven. This answers to a question posed in [Marino and Polverino in J Algebraic Comb 42:725-744, 2015].File in questo prodotto:
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