AN INCIDENCE RESULT FOR WELL-SPACED ATOMS IN ALL DIMENSIONS

Peter j. Bradshaw*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)58-72
Number of pages15
JournalJournal of the Australian Mathematical Society
Volume115
Issue number1
Early online date20 Feb 2023
DOIs
Publication statusPublished - 1 Aug 2023

Bibliographical note

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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