Problems
No person has reviewed any of this; every judgement here is a machine's.
For a designated face of an undirected unweighted planar graph, how many distinct distance patterns can vertices have? Li and Parter (STOC 2019) proved an upper bound; Mozes, Wallheimer and Weimann conjectured the true answer matches their…
Is the number of nonnesting permutations of 1,1,…,n,n avoiding both 1132 and 3312 equal to 3^n - 3 · 2^n-1 + 1 for every n ≥ 1?
A polynomial-time algorithm for computing an optimal committee under any Thiele voting rule on the Voter Interval domain, resolving a ten-year-old open problem posed for Proportional Approval Voting by Elkind and Lackner and later extended…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Does the analytic Bertini restriction theorem for multiplier ideals hold locally, outside a pluripolar exceptional set of fibers? Proved in full generality.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
What is the minimax optimal error rate for density estimation when observations are perturbed by Wasserstein-bounded contaminations? Chao and Dobriban's 2023 preprint left a gap between upper and lower bounds; the sharp rate is now…
Let X = (X_1,…,X_n) be a centered Gaussian vector, not necessarily nondegenerate. Then, for every α_1,…,α_n > 0, E[∏_i=1^n |X_i|^α_i] ≥ ∏_i=1^n E[|X_i|^α_i]. Moreover, if Var(X_i) > 0 for every i, then equality holds if and only if…
Can a noetherian ring have a local cohomology module whose support is not closed - equivalently, one with infinitely many minimal primes? Huneke and Lyubeznik asked; the paper constructs such rings, so the answer is yes.
An asymptotic formula for p(k), the limiting probability that a random permutation has an invariant set of size k: it is asymptotically k^-δ(1+o(1)) times a smooth positive function, sharpening a line of estimates running through…
The multivariate independence polynomial is the partition function of the hard-core model with per-vertex fugacities. The paper proves a lower bound extending to the multivariate setting a result Tao proved in the univariate case, and…
Denjoy's 1932 theorem says a C^1+bv circle diffeomorphism with irrational rotation number has no wandering interval. Whether it is sharp in regularity: for every concave modulus of continuity ω weaker than Lipschitz, there is a C^1+ω…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For positive integers d and k, let n_k(d) be the maximum order of a graph of maximum degree at most d and diameter at most k. It is shown that lim_d → ∞n_k(d)/d^k = 1 for every fixed k, thereby resolving the asymptotic degree-diameter…
In the list update problem, is the simple transposition rule optimal under IID requests? The question traces to Rivest's 1976 study of self-organizing lists. The paper proves transposition is within a small constant factor of the optimal…
Erdos Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system. The answer is exactly the class generated from private-vertex expansions of finite bipartite graphs by finite disjoint unions and…
Treglown conjectured, in a complementary form, that for every positive integer k every digraph D with mind^+(v), d^-(v) ≤ k-1 for all v has an equitable acyclic k-colouring. This implies the acyclic colouring versions of the…
Whether perfectly complete quantum key agreement can be built from quantumly secure one-way functions in a black-box way. It cannot: for any protocol where Alice and Bob exchange only classical messages, make at most q_A and q_B quantum…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
A Banach space is primary if in every decomposition into two complemented subspaces one summand is isomorphic to the whole. Lechner, Motakis, Müller and Schlumprecht identified the primariness of L_p(L_1) as a prominent remaining open…