Orbits and incidence matrices for points, planes and lines regarding the twisted cubic in PG(3,q), q = 2, 3, 4
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910227733938176 |
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| author | Davydov, Alexander A. Marcugini, Stefano Pambianco, Fernanda |
| author_facet | Davydov, Alexander A. Marcugini, Stefano Pambianco, Fernanda |
| contents | In the three-dimensional projective space PG(3,q) over the finite field F_q with q elements, we consider the normal rational curve known as a twisted cubic and the projectivity group G_q that fixes it. For q = 2, 3, 4, we solve the open problems of classifying the orbits of points, planes, and lines under G_q and of determining the corresponding incidence matrices between points, planes, and lines partitioned into these orbits. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_14628 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbits and incidence matrices for points, planes and lines regarding the twisted cubic in PG(3,q), q = 2, 3, 4 Davydov, Alexander A. Marcugini, Stefano Pambianco, Fernanda Combinatorics 51E21, 51E22 In the three-dimensional projective space PG(3,q) over the finite field F_q with q elements, we consider the normal rational curve known as a twisted cubic and the projectivity group G_q that fixes it. For q = 2, 3, 4, we solve the open problems of classifying the orbits of points, planes, and lines under G_q and of determining the corresponding incidence matrices between points, planes, and lines partitioned into these orbits. |
| title | Orbits and incidence matrices for points, planes and lines regarding the twisted cubic in PG(3,q), q = 2, 3, 4 |
| topic | Combinatorics 51E21, 51E22 |
| url | https://arxiv.org/abs/2604.14628 |