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 includes an essential part of all O_6 orbits, whose complete classification is an open problem.
Incidence matrices for the class O6 of lines external to the twisted cubic in PG(3, q)
Stefano Marcugini;Fernanda Pambianco.
2023
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 includes an essential part of all O_6 orbits, whose complete classification is an open problem.File in questo prodotto:
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