Fractional Sylvester–Gallai theorems

DOI10.1073/pnas.1203737109zbMath1292.52014OpenAlexW2053997972WikidataQ47098669 ScholiaQ47098669MaRDI QIDQ5170981

Avi Wigderson, Zeev Dvir, Amir Yehudayoff, Boaz Barak

Publication date: 25 July 2014

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.1203737109

Mathematics Subject Classification ID

Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Erd?s problems and related topics of discrete geometry (52C10)

Related Items (9)

A generalized Sylvester–Gallai-type theorem for quadratic polynomials ⋮ On the number of ordinary lines determined by sets in complex space ⋮ Spanoids---An Abstraction of Spanning Structures, and a Barrier for LCCs ⋮ Interactions of computational complexity theory and mathematics ⋮ Sylvester-Gallai type theorems for quadratic polynomials ⋮ Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via operator scaling ⋮ Sylvester-Gallai for arrangements of subspaces ⋮ Spanoids - An Abstraction of Spanning Structures, and a Barrier for LCCs ⋮ A generalized sylvester-gallai type theorem for quadratic polynomials

Cites Work

• A resolution of the Sylvester-Gallai problem of J.-P. Serre
• Sylvester-Gallai theorems for complex numbers and quaternions
• Perturbed Identity Matrices Have High Rank: Proof and Applications
• A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices
• A Generalization of a Theorem of Sylvester on the Lines Determined by a Finite Point Set.
• A deterministic strongly polynomial algorithm for matrix scaling and approximate permanents

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