English

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 δ\delta-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

R2 v1 2026-07-01T08:49:29.163Z