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math.CO2026
Pappus configurations in the Hall plane
Stefano Lia, John Sheekey, Geertrui Van de Voorde
In this paper, we investigate Pappus configurations in the finite affine Hall plane. In particular, we show that for any two lines and for any triple of points on $…
math.CO2026
Generalising Latin square orthogonality and Frobenius-König with alternating sign matrices
Alena Ernst, Stefano Lia, Cian O'Brien +2
The theory of Latin squares has a long history. While the objects themselves appeared earlier, the study of their general mathematical theory dates back to Euler in the 18th centur…
cs.SC2026
Computational Explorations on Semifields
Jean-Guillaume Dumas, Stefano Lia, John Sheekey
A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small sem…