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Open Problems


TitleAuthor(s)Imp.¹Rec.²Area » Topic » Subtopicsort iconPosted by
trace inequality✭✭0AlgebraMiwa Lin
Elementary symmetric of a sum of matrices✭✭✭0Algebrarscosa
Finite Lattice Representation Problem✭✭✭✭0Algebrawilliamdemeo
inverse of an integer matrixGregory✭✭0Algebralvoyster
Picking up Beats Studio Camouflage blue - Red Diamond✭✭0Algebraviolet
Important Tips to Beats Studio Camouflage blue - White Diamond✭✭0Algebraviolet
Great Known Works Of Beats Studio Camouflage brown - Blue Diamond✭✭0Algebraviolet
$C^r$ Stability ConjecturePalis; Smale✭✭✭✭0Analysism n
Invariant subspace problem✭✭✭0Analysistchow
Criterion for boundedness of power seriesRüdinger✭1Analysisandreasruedinger
Something like Picard for 1-formsElsner✭✭0AnalysisMathOMan
Inequality for square summable complex series Retkes✭✭1Analysistigris35711
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
Sequence defined on multisetsErickson✭✭1CombinatoricsMartin Erickson
Square achievement game on an n x n gridErickson✭✭1CombinatoricsMartin Erickson
Transversal achievement game on a square gridErickson✭✭1CombinatoricsMartin Erickson
Length of surreal productGonshor✭1CombinatoricsLukáš Lánský
Perfect 2-error-correcting codes over arbitrary finite alphabets.✭✭0Combinatorics » Codesdavidcullen
Combinatorial covering designsGordon; Mills; Rödl; Schönheim✭0Combinatorics » DesignsPseudonym
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
Difference between neighbors in a matrixVadim Lioubimov✭✭1Combinatorics » MatricesVadim Lioubimov
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
Ding's tau_r vs. tau conjectureDing✭✭✭0Combinatorics » Optimizationmdevos
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
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

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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