Curves, points, incidences and covering
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911247792865280 |
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| author | Bishnu, Arijit Francis, Mathew Majumder, Pritam |
| author_facet | Bishnu, Arijit Francis, Mathew Majumder, Pritam |
| contents | Given a point set, mostly a grid in our case, we seek upper and lower bounds on the number of curves that are needed to cover the point set. We say a curve covers a point if the curve passes through the point. We consider such coverings by monotonic curves, lines, orthoconvex curves, circles, etc. We also study a problem that is converse of the covering problem -- if a set of $n^2$ points in the plane is covered by $n$ lines then can we say something about the configuration of the points? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21758 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curves, points, incidences and covering Bishnu, Arijit Francis, Mathew Majumder, Pritam Combinatorics Computational Geometry Discrete Mathematics Given a point set, mostly a grid in our case, we seek upper and lower bounds on the number of curves that are needed to cover the point set. We say a curve covers a point if the curve passes through the point. We consider such coverings by monotonic curves, lines, orthoconvex curves, circles, etc. We also study a problem that is converse of the covering problem -- if a set of $n^2$ points in the plane is covered by $n$ lines then can we say something about the configuration of the points? |
| title | Curves, points, incidences and covering |
| topic | Combinatorics Computational Geometry Discrete Mathematics |
| url | https://arxiv.org/abs/2507.21758 |