Orbits of Lines for a Twisted Cubic in PG(3, q)

被引：0

作者：

Davydov, Alexander A. ^{[1
]}

Marcugini, Stefano ^{[2
]}

Pambianco, Fernanda ^{[2
]}

机构：

[1] Russian Acad Sci, Inst Informat Transmiss Problems, Kharkevich Inst, Moscow 127051, Russia

[2] Perugia Univ, Dept Math & Comp Sci, I-06123 Perugia, Italy

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 03期

关键词：

Twisted cubic; projective space; orbits of lines; finite geometry;

D O I：

10.1007/s00009-023-02279-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the projective space PG(3, q), we consider the orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of PG(3, q) are partitioned into classes, each of which is a union of line orbits. In this paper, all classes of lines consisting of a unique orbit are found. For the remaining line types, with one exception, it is proved that they consist exactly of two or three orbits; sizes and structures of these orbits are determined. Also, the subgroups of the stabilizer group of the twisted cubic fixing lines of the orbits are obtained. Problems which remain open for one type of lines are formulated and, for 5 <= q <= 37 and q = 64, a solution is provided.

引用

页数：21

共 22 条

[1] Davydov AA, 2021, Arxiv, DOI arXiv:2103.12655
[2] On planes through points off the twisted cubic in PG(3, q) and multiple covering codes
Bartoli, Daniele
Davydov, Alexer A.
Marcugini, Stefano
Pambianco, Ferna
[J]. FINITE FIELDS AND THEIR APPLICATIONS, 2020, 67
[3] Blokhuis A, 2021, Arxiv, DOI arXiv:2103.16904
[4] The twisted cubic in PG(3, q) and translation spreads in H(q)
Bonoli, G
Polverino, O
[J]. DISCRETE MATHEMATICS, 2005, 296 (2-3) : 129 - 142
[5] The Magma algebra system .1. The user language
Bosma, W
Cannon, J
Playoust, C
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) : 235 - 265
[6] Bruen AA., 1977, GEOMETRIAE DEDICATA, V6, P495, DOI [DOI 10.1007/BF00147786, 10.1007/BF00147786]
[7] ON THE UNIQUENESS OF (2H+1)4-ARCS OF PG(4,2H), H GREATER-THAN-OR-EQUAL-TO 3
CASSE, LRA
GLYNN, DG
[J]. DISCRETE MATHEMATICS, 1984, 48 (2-3) : 173 - 186
[8] Casse LRA., 1982, GEOMETRIAE DEDICATA, V13, P157, DOI [10.1007/BF00147659, DOI 10.1007/BF00147659]
[9] Casse LRA, 2006, PROJECTIVE GEOMETRY, V1109, P51001
[10] Cossidente A., 1997, AUSTRAL J COMBIN, V16, P99

← 1 2 3 →