More pointsets with many rich lines
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914087474036736 |
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| author | Currier, Gabriel |
| author_facet | Currier, Gabriel |
| contents | We present some new sharp constructions for the Szemerédi-Trotter theorem. These constructions generalize previous work of Erdős, Elekes, Sheffer and Silier, Guth and Silier, and the author. In the past, arguments showing the optimality of many of these constructions have required some elementary number theory and have been rather technical, thus limiting the scope of the results. We replace these number-theoretic arguments with purely incidence-geometric ones, allowing for simpler proofs and more general results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | More pointsets with many rich lines Currier, Gabriel Combinatorics 52C10, 52C30 We present some new sharp constructions for the Szemerédi-Trotter theorem. These constructions generalize previous work of Erdős, Elekes, Sheffer and Silier, Guth and Silier, and the author. In the past, arguments showing the optimality of many of these constructions have required some elementary number theory and have been rather technical, thus limiting the scope of the results. We replace these number-theoretic arguments with purely incidence-geometric ones, allowing for simpler proofs and more general results. |
| title | More pointsets with many rich lines |
| topic | Combinatorics 52C10, 52C30 |
| url | https://arxiv.org/abs/2510.09769 |