Intersection numbers of the natural embedding of the twisted triality hexagon T(q^3,q) in PG(7,q^3)
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911480768626688 |
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| author | Petit, Sebastian Van de Voorde, Geertrui |
| author_facet | Petit, Sebastian Van de Voorde, Geertrui |
| contents | In this paper, we study and characterise the natural embedding of the twisted triality hexagon T(q^3,q) in PG(7,q^3). We begin by describing the possible intersections of subspaces of PG(7,q^3) with T(q^3,q). Then, we provide conditions on a set of lines L which ensures that L forms the line set of a naturally embedded twisted triality hexagon. This work follows up on similar results for the split Cayley hexagon by J. A. Thas and H. Van Maldeghem (2008) and F. Ihringer (2014). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Intersection numbers of the natural embedding of the twisted triality hexagon T(q^3,q) in PG(7,q^3) Petit, Sebastian Van de Voorde, Geertrui Combinatorics 51E20 51E12 In this paper, we study and characterise the natural embedding of the twisted triality hexagon T(q^3,q) in PG(7,q^3). We begin by describing the possible intersections of subspaces of PG(7,q^3) with T(q^3,q). Then, we provide conditions on a set of lines L which ensures that L forms the line set of a naturally embedded twisted triality hexagon. This work follows up on similar results for the split Cayley hexagon by J. A. Thas and H. Van Maldeghem (2008) and F. Ihringer (2014). |
| title | Intersection numbers of the natural embedding of the twisted triality hexagon T(q^3,q) in PG(7,q^3) |
| topic | Combinatorics 51E20 51E12 |
| url | https://arxiv.org/abs/2511.04931 |