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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.05013 |
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| _version_ | 1866914707977273344 |
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| author | Jackson, Wen-Ai Wild, Peter |
| author_facet | Jackson, Wen-Ai Wild, Peter |
| contents | An O'Nan configuration in a unital is a set of four lines forming a quadrilateral, where the six intersections of pairs of lines are points of the unital. In 2019 Feng and Li elegantly construct O'Nan configurations in orthogonal and Tits Buekenhout-Metz unitals. We extend their work by extending their construction to a Fano plane embedded in the orthogonal Buekenhout-Metz unital of even order. We deduce that there exist O'Nan configurations in orthogonal Buekenhout-Metz unitals different to those of Feng and Li, and make a conjecture about Fano planes embedded in orthogonal Buekenhout-Metz unitals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on Fano Planes in Orthogonal Buekenhout-Metz Unitals of Even Order Jackson, Wen-Ai Wild, Peter Combinatorics An O'Nan configuration in a unital is a set of four lines forming a quadrilateral, where the six intersections of pairs of lines are points of the unital. In 2019 Feng and Li elegantly construct O'Nan configurations in orthogonal and Tits Buekenhout-Metz unitals. We extend their work by extending their construction to a Fano plane embedded in the orthogonal Buekenhout-Metz unital of even order. We deduce that there exist O'Nan configurations in orthogonal Buekenhout-Metz unitals different to those of Feng and Li, and make a conjecture about Fano planes embedded in orthogonal Buekenhout-Metz unitals. |
| title | A Note on Fano Planes in Orthogonal Buekenhout-Metz Unitals of Even Order |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2403.05013 |