PreprintCC BY-SA 4.0arXiv
The linearity Conjecture
Abstract
The Linearity Conjecture states that in the projective plane PG(2,q), q=ph, every minimal blocking set (w.r.t. lines) is a linear point set over some subfield of 𝔽q. This paper contains the proof of the Linearity Conjecture for pe≠ 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 pe=2 is solved. In Part 2 we prove the Linearity Conjecture for pe≥ 5.
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BibTeX
@misc{sziklai2026linearity,
title = {{The linearity Conjecture}},
author = {Peter Sziklai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30503},
eprint = {2610.30503},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30503},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - The linearity Conjecture
AU - Peter Sziklai
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30503
UR - https://arxiv.org/abs/2610.30503
AB - 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 𝔽_q. This paper contains the proof of the Linearity Conjecture for p^e≠ 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≥ 5.
ER -