Mathematics
Open problems, research attempts and community review.
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-3801 Strongly minimal edge cover
- Math-3802 Upper bound on the divisorial gonality of a graph
- Math-3803 Is it true that every graph whose vertices have odd degree greater than one contains a cycle of length 2^(n) for some n
- Math-3804 Suppose G has n vertices and no induced copy of H
- Math-3805 Show that every (1/2+ľ)|E(ő_(n))| edges of the n-cube ő_(n) contains a C_(4) when n is sufficiently large
- Math-3806 What are the (homogeneous adjacency) spectra of the ultracube and the complete hypergraph
- Math-3807 Is it true that the sum of the k largest Laplacian eigenvalues of a graph with m edges is at most k(k+1)/2+m
- Math-3808 Is it possible for a permutation on n symbols to contain exactly n
- Math-3809 A d-dimensional permutation of order n is an n-by-n-by
- Math-3810 Take any positive integer, and apply the following process: (1) divide it by two if it's even, multiply by three and add
- Math-3811 Suppose that S is a set of positive integers with the property that S+S -- that is, all sums of the form s_(1)+s_(2) for
- Math-3812 Suppose k runners having distinct constant speeds start at a common point and run laps on a unit length circular track
- Math-3813 Show that there is some B so that no integer appears more than B times among the binomial coefficients
- Math-3814 There is no n so that the only integer m with phi(n) = phi(m) is m=n
- Math-3815 Is there a dense of points in the real plane so that every two points are at a rational distance
- Math-3816 Is there a prime between n^(2)and (n+1)^(2 )for every n > 0
- Math-3817 For each k and every sufficiently large n with k dividing ((n-1) choose (k-1)), there is a universal cycle for the k-sub
- Math-3818 Let G be a bicolored graph, and let H be the graph whose vertices are the valid pressing sequences of G and whose edges
- Math-3819 Dittert–Hajek conjecture
- Math-3820 Minimum length of a superpermutation
- Math-3821 Rudin's conjecture on squares in progressions
- Math-3822 Exact Dedekind numbers
- Math-3823 Conjectural Large Genus Asymptotics of Masur–Veech Volumes
- Math-3824 Conjectural Large Genus Asymptotics of Area Siegel–Veech Constants
- Math-3825 Multiplicity-one support of area Siegel–Veech constants
- Math-3826 Bounded wandering domains of entire functions
- Math-3827 Finiteness of Newtonian equilibrium points
- Math-3828 Modified Cartan conjecture
- Math-3829 Few inflection points of holomorphic curves
- Math-3830 Point-hyperplane incidences
- Math-3831 Integer-distance point sets
- Math-3832 Packing reciprocal rectangles in a square
- Math-3833 Classification of Finite Metric Spaces and Combinatorics of Convex Polytopes
- Math-3834 N-body problem
- Math-3835 Periods of Pseudo-Integrable Billiards
- Math-3836 Pisot substitution conjecture
- Math-3837 Nivat's conjecture
- Math-3838 Reversible equivariant planar differential systems
- Math-3839 An extended Poncelet problem I
- Math-3840 An extended Poncelet problem II
- Math-3841 Multiple ergodic averages — Problem 1
- Math-3842 Multiple ergodic averages — Problem 3
- Math-3843 Multiple ergodic averages — Problem 9
- Math-3844 Multiple ergodic averages — Problem 13
- Math-3845 Multiple ergodic averages — Problem 17
- Math-3846 Multiple ergodic averages — Problem 22
- Math-3847 Multiple ergodic averages — Problem 24
- Math-3848 Multiple ergodic averages — Problem 30
- Math-3849 Multiple ergodic averages — Problem 32
- Math-3850 Multiple ergodic averages — Problem 34