Abstract
We prove an incidence result counting the k-rich δ -tubes induced by a well-spaced set of δ-atoms. Our result coincides with the bound that would be heuristically predicted by the Szemerédi–Trotter theorem and holds in all dimensions d≥2 . We also prove an analogue of Beck’s theorem for δ-atoms and δ -tubes as an application of our result.
| Original language | English |
|---|---|
| Pages (from-to) | 58-72 |
| Number of pages | 15 |
| Journal | Journal of the Australian Mathematical Society |
| Volume | 115 |
| Issue number | 1 |
| Early online date | 20 Feb 2023 |
| DOIs | |
| Publication status | Published - 1 Aug 2023 |
Bibliographical note
Publisher Copyright:© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.