Combinatorics
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-2096 What is the length of the shortest sequence in [n]* containing, as a (consecutive) subword, each permutation of [n]
- Math-2097 ("Diamond-Free Posets Problem") What is the size of the largest subset of the Boolean lattice B_(n) which includes no B_
- Math-2098 For any poset P, define ex(n,P) to be the size of the largest subset of the Boolean lattice B_(n) which includes no (inj
- Math-2099 "1/3 - 2/3 Conjecture" For every poset that is not a chain, there is some pair of elements x and y so that x appears abo
- Math-2103 A covering code of radius R is a set of binary n-words so that every binary n-word can be reached from one of the codewo
- Math-2104 An asymmetric covering code of radius R is a set of binary n-words so that every binary n-word can be reached from one o
- Math-2105 An asymmetric packing code of radius R is a set of binary n-words so that no binary n-word can be reached from more than
- Math-2106 A de Bruijn covering code of radius R is a binary string so that the set of words appearing as n consecutive symbols (wi
- Math-2107 There is (essentially) a unique sequence over {1,2} which is its own run-length encoding
- Math-2108 Consider p(v, t), the probability that a walk beginning from the origin ends at the point v on the d-dimensional integer
- Math-2109 What is the threshold function n = f(k) for the event that a random permutation on n symbols contains all patterns on k
- Math-2110 What is the probability that a random nXn matrix over Z_(p) has zero permanent as n goes to infinity
- Math-2111 Let f(p;n,k) = C(n,k) p^(k) (1-p)^(n-k)
- Math-2150 Conjecture of multiplicative persistence
- Math-2151 The 196 conjecture
- Math-2164 Monochromatic Triangles
- Math-2222 How many colors is it necessary to use so that, if you paint every single point of the two-dimensional plane some color
- Math-2223 A set of points S is Euclidean Ramsey if, for every k, there exists an N so that every k-coloring of Euclidean N-space c
- Math-2225 Exact van der Waerden numbers
- Math-2230 Distances among Point Sets in $\mathbb{R}^2$ and $\mathbb{R}^3$
- Math-2274 Steinitz prefix bounds for arbitrary norms
- Math-2275 Cycle--clique Ramsey numbers and an endpoint-fan certificate
- Math-2276 A four-point Hamming barrier in Euclidean Ramsey theory
- Math-2277 Four concyclic points and bounded Euclidean Ramsey witnesses
- Math-2278 van der Waerden numbers and sparse forcing sets
- Math-2279 Polynomial growth of diagonal van der Waerden numbers
- Math-2313 Strongly Balanced Almost-Uniform Vector Permutations
- Math-2337 Ramsey Sets and Finite Transitive Embeddings
- Math-2376 Euclidean Ramsey Configurations and Sphericity
- Math-2399 Enumeration of Graphs with Prescribed Degree Sequences
- Math-2418 Packing and Covering for Infinite Matroids
- Math-2491 The Graphic Kahn–Kalai Conjecture
- Math-2597 Deterministic polynomial construction of strong thin spanning trees
- Math-2598 Barker-sequence length conjecture
- Math-2599 Borsuk covering assertion in dimension nine
- Math-2600 Bounded-degree coboundary expanders in each dimension at least three
- Math-2601 Circulant Hadamard conjecture
- Math-2602 Logarithmic correspondence-coloring bound for fixed forbidden cliques
- Math-2603 Colin de Verdière chromatic-number conjecture
- Math-2604 Deterministic nonbipartite Ramanujan graphs in every fixed degree
- Math-2605 Fractional chromatic number versus ordinary Hadwiger number
- Math-2606 Gopalan–Servedio square-root-degree Fourier bound
- Math-2607 Shareshian–Wachs elementary positivity for chromatic quasisymmetric functions
- Math-2608 Graph decomposition at the integral expectation threshold
- Math-2609 Log-squared sharp threshold for monotone graph properties
- Math-2610 Power improvement for planar halving lines
- Math-2611 Power improvement over exponent two in Heilbronn triangle constructions
- Math-2612 Optimal-order distinct distances in every dimension at least three
- Math-2613 Uniform variance-influence bound for hypergraph properties
- Math-2614 Integral and fractional expectation thresholds within a constant factor