Threshold functions for incidence properties in finite vector spaces

DOI10.1016/j.ffa.2022.102149OpenAlexW4315476267MaRDI QIDQ2689352

Jeong Han Kim, Thang Pham, Semin Yoo, Ben D. Lund

Publication date: 10 March 2023

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.12801

zbMATH Keywords

blocking setsincidencescollinear triplesrich-flats

Mathematics Subject Classification ID

Blocking sets, ovals, (k)-arcs (51E21) Erd?s problems and related topics of discrete geometry (52C10) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40)

Cites Work

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• On point-line incidences in vector spaces over finite fields
• Progression-free sets in \(\mathbb{Z}_4^n\) are exponentially small
• On large subsets of \(\mathbb{F}_q^n\) with no three-term arithmetic progression
• The Szemerédi-Trotter type theorem and the sum-product estimate in finite fields
• Threshold functions
• On the spectrum of minimal blocking sets in \(\text{PG}(2,q)\)
• Thresholds versus fractional expectation-thresholds
• Threshold functions for substructures in random subsets of finite vector spaces
• Incidence Bounds for Block Designs
• On Two-Point Configurations in a Random Set
• Finite Field Kakeya and Nikodym Sets in Three Dimensions

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