Top Open Problems
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-2101 What is the minimum number of n-simplexes needed to triangulate the n-cube
- Math-2102 The "cycle double cover conjecture" states that every bridgeless graph contains a set of cycles which cover each edge of
- Math-2103 "Seymour's Second Neighborhood Conjecture" Any oriented graph has a vertex whose outdegree is at most its second outdegr
- Math-2104 Suppose that G is a tree
- Math-2105 A graph G is said to be uniquely H-saturated if it contains no H, but adding any edge to G creates exactly one copy of H
- Math-2106 Given a permutation σ, what is the maximum number of copies of σ that a permutation on n symbols may contain
- Math-2107 Given two permutations σ and τ, what is the expected number of copies of σ in a permutation chosen uniformly at random f
- Math-2108 Show that the inversion permutation, i
- Math-2109 What is the length of the shortest sequence in [n]* containing, as a (consecutive) subword, each permutation of [n]
- Math-2110 ("Diamond-Free Posets Problem") What is the size of the largest subset of the Boolean lattice B_(n) which includes no B_
- Math-2111 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-2112 "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-2113 Show that there exists a B so that, for every n > 0, there exists a k relatively prime to n whose continued fraction has
- Math-2114 If F is a finite field with at least 4 elements and A is an invertible n by n matrix over F, then there are vectors x, y
- Math-2115 Is x^(2)+y^(2)=z^(2) partition regular
- Math-2116 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-2117 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-2118 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-2119 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-2120 There is (essentially) a unique sequence over {1,2} which is its own run-length encoding
- Math-2121 Consider p(v, t), the probability that a walk beginning from the origin ends at the point v on the d-dimensional integer
- Math-2122 What is the threshold function n = f(k) for the event that a random permutation on n symbols contains all patterns on k
- Math-2123 What is the probability that a random nXn matrix over Z_(p) has zero permanent as n goes to infinity
- Math-2124 Let f(p;n,k) = C(n,k) p^(k) (1-p)^(n-k)
- Math-2125 Order of mixing
- Math-2126 Mixing of all orders
- Math-2127 Typical group automorphisms
- Math-2128 Range of the dimension representation
- Math-2129 Stochastic zeta functions
- Math-2130 Beta functions
- Math-2131 Bernoulli factors of group shifts
- Math-2132 Classify group shifts
- Math-2133 Markov random fields and Bernoulli shifts
- Math-2134 Finitary images of IID processes
- Math-2135 Decidability problems in symbolic dynamics
- Math-2136 Virtual FOG conjecture
- Math-2137 Amenable Cantor actions
- Math-2138 Low degree rigid systems
- Math-2139 Systems with homogeneous components I
- Math-2140 Systems with homogeneous components II
- Math-2141 Low-degree classical Liénard systems
- Math-2142 Periodic Riccati differential equations
- Math-2143 Trigonometric Abel differential equations I
- Math-2144 Trigonometric Abel differential equations II
- Math-2145 A new Hilbert sixteenth-type problem
- Math-2146 A second-order differential equation
- Math-2147 Number of centers
- Math-2148 Periodic rational difference equations
- Math-2149 A class of Hamiltonian systems
- Math-2150 Period functions for systems with homogeneous components