Year: 2026
Type: preprint
Abstract: The Linearity Conjecture states that in the projective plane PG(2,$q$), $q=p^h$, every minimal blocking set (w.r.t. lines) is a linear point set over some subfield of ${\mathbb F}_q$. This paper contains the proof of the Linearity Conjecture for $p^e\ne 3,4$, where $e$ is the exponent of the blocking set. The text contains 3 concatenated parts. In Part 0, we give a guide for reading Parts 1 and 2. Part 1 develops a great part of the method, and the case $p^e=2$ is solved. In Part 2 we prove the Linearity Conjecture for $p^e\geq 5$.
Source: arXiv (Cornell University)
Author: Sziklai, Peter
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223347360