Arcs, Caps and Generalisations in a Finite Projective Space
Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. This paper also contains recent results and several open problems.
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/9/1489 |
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| author | James W. P. Hirschfeld Joseph A. Thas |
| author_facet | James W. P. Hirschfeld Joseph A. Thas |
| author_sort | James W. P. Hirschfeld |
| collection | DOAJ |
| description | Arcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. This paper also contains recent results and several open problems. |
| format | Article |
| id | doaj-art-cfe54815b22b46e29cc8c862ce20089b |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-cfe54815b22b46e29cc8c862ce20089b2025-08-20T01:49:28ZengMDPI AGMathematics2227-73902025-04-01139148910.3390/math13091489Arcs, Caps and Generalisations in a Finite Projective SpaceJames W. P. Hirschfeld0Joseph A. Thas1Department of Mathematics, University of Sussex, Brighton BN1 9QH, UKDepartment of Mathematics, Ghent University, 9000 Gent, BelgiumArcs and caps are fundamental structures in finite projective spaces. They can be generalised. Here, a survey is given of some important results on these objects, in particular on generalised ovals and generalised ovoids. This paper also contains recent results and several open problems.https://www.mdpi.com/2227-7390/13/9/1489arccapgeneralised ovalgeneralised ovoidtranslationfinite projective space |
| spellingShingle | James W. P. Hirschfeld Joseph A. Thas Arcs, Caps and Generalisations in a Finite Projective Space Mathematics arc cap generalised oval generalised ovoid translation finite projective space |
| title | Arcs, Caps and Generalisations in a Finite Projective Space |
| title_full | Arcs, Caps and Generalisations in a Finite Projective Space |
| title_fullStr | Arcs, Caps and Generalisations in a Finite Projective Space |
| title_full_unstemmed | Arcs, Caps and Generalisations in a Finite Projective Space |
| title_short | Arcs, Caps and Generalisations in a Finite Projective Space |
| title_sort | arcs caps and generalisations in a finite projective space |
| topic | arc cap generalised oval generalised ovoid translation finite projective space |
| url | https://www.mdpi.com/2227-7390/13/9/1489 |
| work_keys_str_mv | AT jameswphirschfeld arcscapsandgeneralisationsinafiniteprojectivespace AT josephathas arcscapsandgeneralisationsinafiniteprojectivespace |