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Threshold functions for incidence properties in finite vector spaces
- Publication Year :
- 2022
-
Abstract
- The main purpose of this paper is to provide threshold functions for the events that a random subset of the points of a finite vector space has certain properties related to point-flat incidences. Specifically, we consider the events that there is an $\ell$-rich $m$-flat with regard to a random set of points in $\mathbb{F}_q^n$, the event that a random set of points is an $m$-blocking set, and the event that there is an incidence between a random set of points and a random set of $m$-flats. One of our key ingredients is a stronger version of a recent result obtained by Chen and Greenhill (2021).<br />Comment: 17 pages
- Subjects :
- Mathematics - Combinatorics
52C10, 05D40
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2203.12801
- Document Type :
- Working Paper