Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type

DOI10.19086/da.18361zbMath1456.52026arXiv1911.09019OpenAlexW3117099148MaRDI QIDQ5144434

Anthony Carbery, Marina Iliopoulou

Publication date: 16 January 2021

Published in: discrete Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.09019

zbMATH Keywords

family of linesfamily of \(k\)-planesKakeya-type estimate

Mathematics Subject Classification ID

Planar arrangements of lines and pseudolines (aspects of discrete geometry) (52C30) Other finite incidence structures (geometric aspects) (51E30)

Related Items (5)

Joints of varieties ⋮ Incidence bounds on multijoints and generic joints ⋮ Multijoints and factorisation ⋮ Joints tightened ⋮ Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type

Cites Work

• Unnamed Item
• On the Erdős distinct distances problem in the plane
• Counting multijoints
• On lines and joints
• A proof of the multijoints conjecture and Carbery's generalization
• Extremal problems in discrete geometry
• Counting and cutting cycles of lines and rods in space
• Algebraic methods in discrete analogs of the Kakeya problem
• Algebraic combinatorial geometry: the polynomial method in arithmetic combinatorics, incidence combinatorics, and number theory
• On lines, joints, and incidences in three dimensions
• Colouring multijoints
• On the size of Kakeya sets in finite fields
• The Joints Problem in $\mathbb{R}^n$
• THE KAKEYA SET AND MAXIMAL CONJECTURES FOR ALGEBRAIC VARIETIES OVER FINITE FIELDS
• Counting joints with multiplicities
• Joints formed by lines and a $k$-plane, and a discrete estimate of Kakeya type
• Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers

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