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problems
Among classes of tournaments for which neither hardness nor polynomial-time solvability of isomorphism was known, bounded VC dimension stood out as an open problem of Neuen and Grohe. Resolved: isomorphism of tournaments of VC dimension d…
Dyn and Farkhi conjectured that the squared Hausdorff distance from a compact set to its convex hull is subadditive under Minkowski addition. It holds in dimensions one and two and fails from dimension three; the sharp threshold exponent…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
A dimension-independent subgaussian concentration bound for Gaussian vectors under coordinate-wise nonlinear maps, valid for any bounded function under a well-conditioned covariance, which answers a question of Simone Bombari on sign…
Pak and Slonim conjectured that stretched Schubert structure constants are eventually polynomial. They are. Monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial, and the Schubert duality of…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Pólya conjectured in 1954 that the Weyl-law expression bounds the eigenvalue counting function of the Laplacian. The paper proves the Neumann case for Euclidean balls in dimensions three and higher, extending the authors' earlier planar…
Sixteen previously unknown exact values, plus three that confirm the sibling theorem entries' predictions computationally, across five ordered-pattern families (P^alt, S^sc, C^mon, M^nest, K) under dihedral and reflective group actions -…
For unit-modulus complex numbers z_i, let p_n(z)=∏_i≤ n(z-z_i) and M_n=max_|z|=1|p_n(z)|. Erdős's prize question: is there c>0 with ∑_k≤ n M_k > n^1+c?
Casalaina-Martin and Zhjeqi proved that the first Chern class of every torsion-free coherent quotient of a tensor power of the logarithmic cotangent sheaf is pseudo-effective, noting in Remark 4.5 that torsion-freeness was imposed only for…
How dense can a sum-free subset of the lattice cube 1,…,n^d be? Aydinian and Cameron asked for the limiting density, which is also Problem 6 in Ben Green's list of 100 open problems. The natural conjecture is that the optimum is a slice x…
Does the block 11 occur infinitely often in the base-2 expansion of the Erdős-Borwein constant E = ∑_n ≥ 1 1/2^n - 1? Posed by Crandall in 2012.
In the Frankl-Pach-Erdős circle of VC-dimension problems, the first arXiv version of the paper posed the k=3 case of a witness construction question. ChatGPT 5.4 Pro answered it; the published construction generalizes the model's response,…
The group version of the Matrix Spencer conjecture holds: for every finite group G there are signs ε ∈ ± 1^G with |∑_g ∈ G ε_g ρ(g)| ≤ C√|G|, where ρ is the left regular representation and C is universal.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
For an unkilled Levy process ξ drifting to +∞ with all positive exponential moments, let I_ξ = ∫_0^∞ e^-ξ_t dt and X_ξ = 1/I_ξ. Bertoin and Yor proved X_ξ is moment-determinate when ξ has no positive jumps and conjectured that this…
For a multidimensional reflected diffusion, does the basic adjoint relationship uniquely characterize the stationary distribution? The question had stood unresolved for more than thirty-five years since the BAR approach was introduced. For…
Can any single-pass semi-streaming algorithm beat the naive greedy 1/2-approximation for maximum matching? No. No single-pass semi-streaming algorithm, deterministic or randomized, achieves a better-than-half approximation, so greedy is…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
What is the optimal competitive ratio for online vertex cover when edges arrive one at a time? The paper proves a tight factor-2 lower bound via a reduction in the blueprint framework of Assadi, Jiang and Xiang, closing the gap left by…