2014/09/24 by S. G. Barwick, Wen-Ai Jackson, Barwick, S. G. +2
Computer Science · Mathematics · Medicine · #51E20 #Chronic Lymphocytic Leukemia Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.CO #msc:51E20
paper · pdf · doi:10.48550/arxiv.1409.6794
arxiv created 2014/09/24 · openalex publication_date 2014/09/24 · arxiv updated 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let π be an order-q-subplane of PG(2,q3) that is exterior to ℓ_∞. Then the exterior splash of π is the set of q2+q+1 points on ℓ_∞ that lie on an extended line of π. Exterior splashes are projectively equivalent to scattered linear sets of rank 3, covers of the circle geometry CG(3,q), and hyper-reguli in PG(5,q). In this article we use the Bruck-Bose representation in PG(6,q) to investigate the structure of π, and the interaction between π and its exterior splash. In PG(6,q), an exterior splash \mathbb S has two sets of cover planes (which are hyper-reguli) and we show that each set has three unique transversals lines in the cubic extension PG(6,q3). These transversal lines are used to characterise the carriers of \mathbb S, and to characterise the sublines of \mathbb S.