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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
The Hodge ConjectureHodge✭✭✭✭0Geometry » Algebraic GeometryCharles
A conjecture on iterated circumcentresGoddyn✭✭1Geometrymdevos
Big Line or Big Clique in Planar Point SetsKara; Por; Wood✭✭1GeometryDavid Wood
Average diameter of a bounded cell of a simple arrangementDeza; Terlaky; Zinchenko✭✭0Geometrydeza
Convex 'Fair' Partitions Of Convex PolygonsNandakumar; Ramana✭✭1GeometryNandakumar
Dense rational distance sets in the planeUlam✭✭✭0Geometrymdevos
Simplexity of the n-cube✭✭✭1Geometrymdevos
Kneser–Poulsen conjectureKneser; Poulsen✭✭✭0Geometrytchow
Erdös-Szekeres conjectureErdos; Szekeres✭✭✭0Geometrymdevos
Monochromatic empty triangles✭✭✭0Geometrymdevos
Inequality of the means✭✭✭0Geometrymdevos
Edge-Colouring Geometric Complete GraphsHurtado✭✭1GeometryDavid Wood
Partition of Complete Geometric Graph into Plane Trees✭✭0GeometryDavid Wood
Point sets with no empty pentagonWood✭1GeometryDavid Wood
Covering a square with unit squares✭✭0GeometryMartin Erickson
Convex uniform 5-polytopes✭✭1GeometryACW
Partitioning the Projective PlaneNoel✭✭1GeometryJon Noel
Dirac's ConjectureDirac✭✭0GeometryDavid Wood
General position subsetsGowers✭✭0GeometryDavid Wood
Generalised Empty Hexagon ConjectureWood✭✭1GeometryDavid Wood
Chromatic number of associahedronFabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood✭✭1GeometryDavid Wood
Convex Equipartitions with Extreme PerimeterNandakumar✭✭1GeometryNandakumar
Edge-Unfolding Convex PolyhedraShephard✭✭0GeometryErik Demaine
Diagonal Ramsey numbersErdos✭✭✭✭0Combinatorics » Ramsey Theorymdevos
The large sets conjectureBrown; Graham; Landman✭✭✭0Combinatorics » Ramsey Theoryvjungic
Concavity of van der Waerden numbersLandman✭✭0Combinatorics » Ramsey TheoryBruce Landman
Edge-antipodal colorings of cubesNorine✭✭0Combinatorics » Ramsey Theorymdevos
Saturated $k$-Sperner Systems of Minimum SizeMorrison; Noel; Scott✭✭1Combinatorics » PosetsJon Noel
Ding's tau_r vs. tau conjectureDing✭✭✭0Combinatorics » Optimizationmdevos
Rota's unimodal conjectureRota✭✭✭0Combinatorics » Matroid Theorymdevos
Bases of many weightsSchrijver; Seymour✭✭✭0Combinatorics » Matroid Theorymdevos
Aharoni-Berger conjectureAharoni; Berger✭✭✭0Combinatorics » Matroid Theorymdevos
Equality in a matroidal circumference boundOxley; Royle✭✭0Combinatorics » Matroid TheoryGordon Royle
A nowhere-zero point in a linear mappingJaeger✭✭✭0Combinatorics » Matricesmdevos
The additive basis conjectureJaeger; Linial; Payan; Tarsi✭✭✭0Combinatorics » Matricesmdevos
The permanent conjectureKahn✭✭0Combinatorics » Matricesmdevos
The Alon-Tarsi basis conjectureAlon; Linial; Meshulam✭✭0Combinatorics » Matricesmdevos
Rota's basis conjectureRota✭✭✭0Combinatorics » Matricesmdevos
Combinatorial covering designsGordon; Mills; Rödl; Schönheim✭0Combinatorics » DesignsPseudonym
Perfect 2-error-correcting codes over arbitrary finite alphabets.✭✭0Combinatorics » Codesdavidcullen
Long rainbow arithmetic progressionsFox; Jungic; Mahdian; Nesetril; Radoicic✭✭0Combinatoricsvjungic
Rainbow AP(4) in an almost equinumerous coloringConlon✭✭0Combinatoricsvjungic
Monotone 4-term Arithmetic ProgressionsDavis; Entringer; Graham; Simmons✭✭0Combinatoricsvjungic
Even vs. odd latin squaresAlon; Tarsi✭✭✭0Combinatoricsmdevos
2-accessibility of primesLandman; Robertson✭✭0Combinatoricsvjungic
3-accessibility of Fibonacci numbersLandman; Robertson✭✭0Combinatoricsvjungic
Wide partition conjectureChow; Taylor✭✭0Combinatoricstchow
Shuffle-Exchange ConjectureBeneš; Folklore; Stone✭✭✭0CombinatoricsVadim Lioubimov
Beneš ConjectureBeneš✭✭✭0CombinatoricsVadim Lioubimov
Dividing up the unrestricted partitionsDavid S.; Newman✭✭0CombinatoricsDavidSNewman

Imp.¹: Importance (Low ✭, Medium ✭✭, High ✭✭✭, Outstanding ✭✭✭✭)
Rec.²: Recommended for undergraduates.

Note: Resolved problems from this section may be found in Solved problems.

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