New discretised polynomial expander and incidence estimates
Combinatorics
2026-01-21 v2 Classical Analysis and ODEs
Abstract
We present two applications of recent developments in incidence geometry. One is a -discretised version of a particular `Elekes--R\'onyai' expander problem. The second application is an incidence estimate addressing the scenario when both tubes, squares and their shadings satisfy non-concentration assumptions.
Cite
@article{arxiv.2601.01264,
title = {New discretised polynomial expander and incidence estimates},
author = {Ciprian Demeter and William O'Regan},
journal= {arXiv preprint arXiv:2601.01264},
year = {2026}
}
Comments
20 pages, updated references, some typos corrected