Problems
Everything in the archive: the problem as it was posed, what has been attempted against it, and who checked each attempt. The mark down the left of the list says who has looked — a person, a machine, or nobody yet. Human reviews and machine checks are counted separately and are never added together.
104 problems
For D_3(m) = vecC_m square vecC_m square vecC_m, can the full arc set be partitioned into three directed Hamilton cycles for every integer m ≥ 3?
For a pure O-sequence h = (h_0, …, h_e) of codimension three and type two, is h_i^2 ≥ h_i-1 h_i+1 for every interior index i? The stated monomial case is proved; the broader level-Hilbert-function case remains open.
For every finite connected graph, is girth(G) + 1 at most the product of its largest induced-tree order and its second-smallest degree?
Given n and 1 ≤ c ≤ n!, can n distinct group elements be chosen so that their n! ordered products take exactly c distinct values? Constructions realize every c.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Does the Hodge bundle Ω_g over the moduli stack of genus g ≥ 2 curves contain any nontrivial sub-bundles? Posed by Dawei Chen around 2015; the answer is no.
The swap chain flips checkerboard 2×2 blocks to sample 0/1 matrices with fixed row and column sums. Kannan, Tetali and Vempala conjectured in 1997 that it mixes in polynomial time for all feasible margins; the lazy chain is shown to have…
Ji, Li and Wang conjectured in 2024 that every parallel chip-firing game on a finite connected graph whose chip count lies strictly between 2|E|-|V| and 2|E| has period exactly 2, generalizing the middle rung of Levine's devil's staircase…
For |A| = n, how small can the cofactor set Q(A) = a / gcd(a,b) : a, b ∈ A be? The answer is h(n) = n^1/2 + o(1): a new upper bound h(n) ≤ n^1/2 exp(O(√log n)) matches the classical lower bound.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Bounds the weighted sum ∑ 1/(a log a) taken over primitive sets of integers (sets where no element divides another).
Can the critical-exponent relation a + b = 1 at the jamming transition, observed numerically to high precision in the full replica-symmetry-breaking solution of hard spheres, be derived analytically from the scaling equations?
What is the largest A⊆1,…,N such that all subset sums ∑_n∈ S1/n (over S⊆ A) are distinct?
Does there exist a group with more than one but only finitely many maximal locally soluble normal subgroups? An explicit group with exactly two settles it.
For every finite set A⊂ Z with |A|≥ 2, define C(A)=log(|A+A|/|A|)/log(|A-A|/|A|). Determine the largest possible value of C(A), equivalently the least universal exponent c such that |A+A|/|A| ≤ (|A-A|/|A|)^c for every such set A. The…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Under smoothness, positivity, decay and score assumptions, are all steady solutions of the Coulomb Vlasov-Maxwell-Landau system on T^3 × R^3 necessarily spatially uniform Maxwellians?