OpenAI Math·Subject
Combinatorics
37 of the 372 results in OpenAI's maths catalogue are in combinatorics. Each page quotes OpenAI's own summary, links the preprints and embeds the animation once it is released. 7 of them have a video so far.
Watch
Videos in Combinatorics
0:21Erdős–Gallai Conjecture: Every Graph Splits Into Few Loops
0:20Hypercube Ramsey Conjecture: How Many Dots Force a Cube?
0:21Erdős Conjecture on Arithmetic Progressions: OpenAI Claims a Proof
0:21Ramsey Numbers r(s,t): OpenAI Claims the Sharp Log Exponent
0:40Barnette's Conjecture: Does This Loop Always Exist?
0:40The Harary–Hill Conjecture: Why 18 Dots Need 1008 Crossings
0:455 Maths Problems OpenAI Says Its AI Just Solved
All 37 results
- 155A counterexample to periodic tiling in dimension threeLean
- 156Borsuk's conjecture fails in dimension nineLean
- 157Graph coloring, clique minors, and Colin de Verdière invariantsLean
- 158The Euclidean plane cannot be colored with five colorsVideoLean
- 159Erdős’s reciprocal-sum conjecture and quasipolynomial Szemerédi boundsVideoLean
- 160Superexponential van der Waerden numbersLean
- 161Counterexamples to Sidorenko’s conjecture and the forcing conjectureLean
- 162Counterexamples to Ryser’s covering conjectureLean
- 164Hindman’s finite sums and products conjecture
- 165The Harary–Hill and Zarankiewicz crossing-number formulasWrite-upVideoLean
- 166The higher-dimensional Erdős distinct-distances conjecture
- 167Planar distinct distances and unit-distance boundsLean
- 168Combinatorial invariance of Kazhdan–Lusztig polynomialsLean
- 169Shareshian–Wachs elementary positivityLean
- 170Sharp logarithmic exponents for off-diagonal Ramsey numbersVideoLean
- 171The hypercube Ramsey conjectureVideo
- 172Classification of finite Euclidean Ramsey configurationsLean
- 173Seymour’s second-neighborhood conjectureLean
- 174Deterministic construction of strong thin spanning treesLean
- 175Talagrand’s expectation thresholds, discrete convexity, and graph decompositionsLean
- 176The second Kahn–Kalai conjecture with an edge-count boundLean
- 177Bounded-degree coboundary expandersLean
- 178Deterministic nonbipartite Ramanujan graphs in every fixed degree
- 179The circulant Hadamard and Barker-sequence conjecturesLean
- 180Barnette’s Hamiltonian-cycle conjectureVideoLean
- 181The Erdős–Gallai cycle-decomposition conjectureVideoLean
- 182Power savings for intersective polynomial differences and prime argumentsLean
- 183Power savings for planar halving lines and k-setsLean
- 184Correspondence coloring with a fixed forbidden subgraphLean
- 185Counterexamples to infinite matroid intersection and packing/coveringLean
- 186Uniform influence and sharp thresholds for graph and hypergraph propertiesLean
- 187Snaky in 21 Maker movesLean
- 188The sharp terminal leave in random triangle removalLean
- 189Cycle–clique Ramsey numbersLean
- 190Polynomial removal fails for ordered binary matricesLean
- 191A power improvement in the Heilbronn triangle lower boundLean
- 192Boolean functions violate the square-root degree bound by arbitrary factorsLean
Other subjects
- Theoretical computer science 40
- Algebraic and complex geometry 36
- Number theory 31
- Differential geometry 29
- Probability and statistical mechanics 29
- Mathematical physics 25
- Operator algebras 19
- Algebra 18
- Topology 18
- Partial differential equations 16
- Real and complex analysis 16
- Convex and metric geometry 15
- Group theory 14
- Dynamical systems and ergodic theory 12
- Functional analysis 11
- Mathematical logic 6