Incidence matrices for the class O₆ of lines external to the twisted cubic in PG(3,q)

2022/10/23 by Alexander A. Davydov, Davydov, Alexander A., Stefano Marcugini +3
Engineering · Mathematics · Medicine · #05B25 #05E18 #51E20 #51E21 #51E22 #Chronic Lymphocytic Leukemia Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2210.12821

openalex publication_date 2022/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the structures of the plane-line and point-line incidence matrices of the projective space PG(3,q) connected with orbits of planes, points, and lines under the stabilizer group of the twisted cubic. In the literature, lines are partitioned into classes, each of which is a union of line orbits. In this paper, for all q, even and odd, we determine the incidence matrices connected with a family of orbits of the class named O₆. This class contains lines external to the twisted cubic. The considered family include an essential part of all O₆ orbits, whose complete classification is an open problem.

Related

• Further results on orbits and incidence matrices for the class O₆ of lines external to the twisted cubic in PG(3,q)
• Twisted cubic and plane-line incidence matrix in PG(3,q)
• Twisted cubic and point-line incidence matrix in PG(3,q)
• Orbits of the class O₆ of lines external with respect to the twisted cubic in PG(3,q)
• Twisted cubic and orbits of lines in PG(3,q), II