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A survey of Sylvester's problem and its generalizations
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Singular points in planar finite sets I
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Visibility and parallelotopes in projective space
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A resolution of the sylvester-gallai problem of J.-P. serre
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On representing sylvester-gallai designs
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On some problems of elementary and combinatorial geometry
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On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
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Extremal problems in discrete geometry
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Personal reminiscences and remarks on the mathematical work of Tibor Gallai
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On ordinary points in arrangements
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Some combinational problems in geometry
inferredcites →https://doi.org/10.1016/0097-3165(71)90006-9openalex-snapshot
On the number of ordinary planes
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Some extremal problems in geometry
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Sets for which no point lies on many connecting lines
inferredcites →https://doi.org/10.1016/0097-3165(82)90080-2openalex-snapshot
On monochrome lines and hyperplanes
inferredcites →https://doi.org/10.1016/s0195-6698(83)80036-5openalex-snapshot
A Combinatorial Distinction Between the Euclidean and Projective Planes
inferredcites →https://doi.org/10.1016/s0304-0208(08)72816-0openalex-snapshot
Some Old and New Problems in Combinatorial Geometry
inferredcites →https://doi.org/10.1017/s0305004100043243openalex-snapshot
A characterization of sets of n points which determine n hyperplanes
inferredcites →https://doi.org/10.1080/00029890.1944.11999121openalex-snapshot
Clubs and Allied Activities
inferredcites →https://doi.org/10.1080/00029890.1970.11992442openalex-snapshot
Sylvester's Problem on Collinear Points and a Relative
inferredcites →https://doi.org/10.1080/00029890.1983.11971238openalex-snapshot
A Conjecture Related to Sylvester's Problem
inferredcites →https://doi.org/10.1080/0025570x.1968.11975829openalex-snapshot
Sylvester's Problem on Collinear Points
inferredcites →https://doi.org/10.1080/0025570x.1975.11976510openalex-snapshot
Monochromatic Lines in the Plane
inferredcites →https://doi.org/10.1080/0025570x.1979.11976751openalex-snapshot
Monochrome Lines in the Plane
inferredcites →https://doi.org/10.1090/s0002-9939-1960-0113206-0openalex-snapshot
A Generalization of the Theorem of Sylvester
inferredcites →https://doi.org/10.1090/s0002-9939-1963-0146813-2openalex-snapshot
A Further Theorem of the Sylvester Type
inferredcites →https://doi.org/10.1090/s0002-9939-1984-0733410-4openalex-snapshot
Sylvester's Problem and Motzkin's Theorem for Countable and Compact Sets
inferredcites →https://doi.org/10.1090/s0002-9947-1951-0041447-9openalex-snapshot
The Lines and Planes Connecting the Points of a Finite Set
inferredcites →https://doi.org/10.1093/qmath/2.1.221openalex-snapshot
COLLINEARITY PROPERTIES OF SETS OF POINTS
inferredcites →https://doi.org/10.21236/ad0768893openalex-snapshot
New Views on Some Old Questions of Combinatorial Geometry
inferredcites →https://doi.org/10.2140/pjm.1972.40.617openalex-snapshot
Simple points in pseudoline arrangements
inferredcites →https://doi.org/10.2140/pjm.1983.109.275openalex-snapshot
On Sylvester’s problem and Haar spaces
inferredcites →https://doi.org/10.2307/2315536openalex-snapshot
A Proof of Sylvester's Theorem on Collinear Points
inferredcites →https://doi.org/10.2307/3608586openalex-snapshot
2577. The dual of a well-known theorem
inferredcites →https://doi.org/10.4153/cjm-1958-024-6openalex-snapshot
On the Number of Ordinary Lines Determined by n Points
inferredcites →https://doi.org/10.4153/cjm-1966-039-2openalex-snapshot
Bisecants of Finite Collections of Sets in Linear Spaces
inferredcites →https://doi.org/10.4153/cjm-1980-017-1openalex-snapshot
Sylvester's Problem for Spreads of Curves
inferredcites →https://doi.org/10.4153/cmb-1961-007-7openalex-snapshot
An Enumeration of the Five Parallelohedra
inferredcites →https://doi.org/10.4153/cmb-1966-001-6openalex-snapshot
Extensions of Sylvester's Theorem
inferredcites →https://doi.org/10.4153/cmb-1988-020-2openalex-snapshot
The Solution to a Problem of Grünbaum
inferredcites →https://doi.org/10.7146/math.scand.a-10758openalex-snapshot
A Generalization of a Theorem of Sylvester on the Lines Determined by a Finite Point Set.
inferredcites →https://doi.org/10.7146/math.scand.a-10937openalex-snapshot
Hyperplanes and Lines Associated with Families of Compact Sets in Locally Convex Spaces.
inferredcites →https://doi.org/10.7146/math.scand.a-11884openalex-snapshot
On configurations in 3-space without elementary planes and on the number of ordinary planes.
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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Enumerating Motzkin–Rabin geometries
inferred← citeshttps://doi.org/10.1006/eujc.2000.0446openalex-snapshot
On Unit Circles Which Avoid All but Two Points of a Given Point-set
inferred← citeshttps://doi.org/10.1006/jagm.1998.0979openalex-snapshot
Open Problems Presented at SCG'98
inferred← citeshttps://doi.org/10.1006/jcta.2001.3243openalex-snapshot
On Number of Circles Intersected by a Line
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Projective Configuration Theorems: Old Wine into New Wineskins
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Some Results on Point Visibility Graphs
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Recent Developments in Combinatorial Geometry
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A Simple Divide-and-Conquer Algorithm for Solving an Instance of Planar Convex Hull Problems
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A generalisation of Sylvester’s problem to higher dimensions
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On Matrix Rigidity and Locally Self-Correctable Codes
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Gallai—Sylvester Theorem for Pairwise Intersecting Unit Circles
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Sylvester?Gallai Theorem and Metric Betweenness
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The Sylvester-Chvatal Theorem
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Sylvester–Gallai Theorems for Complex Numbers and Quaternions
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On Sets Defining Few Ordinary Lines
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A Quantitative Variant of the Multi-colored Motzkin–Rabin Theorem
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Sylvester–Gallai for Arrangements of Subspaces
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On Sets Defining Few Ordinary Planes
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On the Number of Ordinary Lines Determined by Sets in Complex Space
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On the Number of Monochromatic Lines in $$\pmb {\mathbb {R}}^d$$
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The Dirac–Goodman–Pollack Conjecture
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On the Structure of Pointsets with Many Collinear Triples
inferred← citeshttps://doi.org/10.1007/s00454-024-00661-xopenalex-snapshot
A Sylvester–Gallai-Type Theorem for Complex-Representable Matroids
inferred← citeshttps://doi.org/10.1007/s00493-024-00112-4openalex-snapshot
Unavoidable Flats in Matroids Representable over Prime Fields
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A constructive version of the Sylvester–Gallai theorem
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On a conjecture of Kelly on (1, 3)-representation of Sylvester–Gallai designs
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On the minimum number of ordinary conics
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The Sylvester–Gallai theorem, colourings and algebra
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In Memoriam: Peter Benjamin Borwein (1953–2020)
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Unexpected hypersurfaces with multiple fat points
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Forbidden Configurations in Discrete Geometry
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SYLVESTER–GALLAI TYPE THEOREMS FOR APPROXIMATE COLLINEARITY
inferred← citeshttps://doi.org/10.1017/fms.2014.2openalex-snapshot
IMPROVED RANK BOUNDS FOR DESIGN MATRICES AND A NEW PROOF OF KELLY’S THEOREM
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A generalized Sylvester–Gallai-type theorem for quadratic polynomials
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An Algorithmic Proof of the Motzkin-Rabin Theorem on Monochrome Lines
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In Search of Melchior’s Ordinary Points
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Bounded Negativity and Arrangements of Lines
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Blackbox Polynomial Identity Testing for Depth 3 Circuits
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From Sylvester-Gallai Configurations to Rank Bounds: Improved Black-Box Identity Test for Depth-3 Circuits
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Radical Sylvester-Gallai Theorem for Cubics
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Computational Geometry Column 34
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Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes
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From sylvester-gallai configurations to rank bounds
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Sylvester-Gallai type theorems for quadratic polynomials
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Strong Algebras and Radical Sylvester-Gallai Configurations
inferred← citeshttps://doi.org/10.1145/777792.777809openalex-snapshot
A tight bound for the number of different directions in three dimensions
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A Reverse Analysis of the Sylvester-Gallai Theorem
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Some Famous Problems of Discrete Geometry
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A generalised Sylvester-Gallai Theorem
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On the Sylvester–Gallai theorem for conics
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A quantitative variant of the multi-colored Motzkin-Rabin theorem
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Sylvester-Gallai for Arrangements of Subspaces
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A generalisation of Sylvester's problem to higher dimensions
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On the Existence of Ordinary Triangles
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On the minimum number of high degree curves containing few points
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Blocking sets in small finite linear spaces
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Some applications of algebraic methods in combinatorial geometry
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Incidence problems in discrete geometry
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