Incidences with Pfaffian Curves and Functions
Combinatorics
2023-11-10 v1
Abstract
We introduce a new approach for studying incidences with non-algebraic curves in the plane. This approach is based on the concepts of Pfaffian curves and Pfaffian functions, as defined by Khovanskii. We derive incidence bounds for curves that are defined with exponentials, logarithms, trigonometric functions, integration, and more. Our bound for incidences with Pfaffian curves matches a classical bound of Pach and Sharir for incidences with algebraic curves, up to polylogarithmic factors.
Keywords
Cite
@article{arxiv.2311.05517,
title = {Incidences with Pfaffian Curves and Functions},
author = {Alexander Balsera},
journal= {arXiv preprint arXiv:2311.05517},
year = {2023}
}
Comments
14 Pages, 7 figures