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R_dih(P_3^alt, K_b) = R_cyc(P_3^alt, K_b) = 2b - 1 for all b ∈ N — the a = 3 slice of Conjecture 4.9 (Damnjanović–Đorđević, arXiv:2607.06817) and Conjecture 4.23 (Bašić–Damnjanović–Stevanović–Stošić, arXiv:2604.16188).

Mason conjectured the following: let M be a matroid of rank r, and let W_i denote the number of flats of M of rank i. Is it true that for all 1 ≤ i ≤ r - 1, we have W_i^2 ≥ W_i + 1W_i - 1? This is false; a counterexample is given by a…

An n-divisor set contains a multiple of every integer from 1 to n. Umans and Wang proposed, as the arithmetic-progression form of their Strong (α,β)-Divisor Conjecture, that such a progression exists with few terms of bounded magnitude,…

The directed five-dimensional torus D_5(m) has a Hamilton decomposition for every odd m ≥ 3, extending the decomposition program for directed tori beyond the three-dimensional case.

Nikolov and Ullman asked, as Open Problem 1 on DifferentialPrivacy.org, whether k statistical queries over a universe of size T can be released under pure differential privacy at the square-root error rate that the known lower bounds…

The Benjamini-Hochberg procedure is known not to control the false discovery rate at its nominal level under arbitrary dependence. A folklore conjecture in the FDR literature held that it must at least control the FDR up to a universal…

Let S(N) count the distinct values of ∑_n∈ A 1/n over A⊆1,…,N. Estimate S(N).

Monical, Tokcan and Yong conjectured that every fixed positive power of the Vandermonde determinant fails to have saturated Newton polytope in sufficiently many variables. For every even power k ≥ 4 there is an explicit lattice point of…

There exists a Hadamard matrix of order 668: a matrix H∈-1,1^668×668 such that HH^ T=668I_668. Equivalently, the 668 rows of H are pairwise orthogonal.

How large can a Bruhat interval in S_n that is a poset hypercube be? Using a permutation pattern suggested by AlphaEvolve, the authors exhibit hypercube intervals of dimension O(n log n) for n a power of 2, matching the largest possible…

Subbarao and Verma asked in 1999 (Problem 5.7, first part) whether the complementary Bell numbers f(n) = B_n(-1) take any given value only finitely many times. Campbell proves they do: for every fixed integer the fiber is finite, a result…

Let n_k be the least n > 2k such that (n-k)(n-k+1)…(n-1) has no prime factor in (k, 2k). Erdos conjectured a superpolynomial lower bound; for all large k, n_k > e^log^2 k / (20 loglog k).

The Gaussian Moments Conjecture asks whether, for complex polynomials P,Q in n independent standard real Gaussian variables, E(P^m)=0 for all m≥ 1 forces E(QP^m)=0 for all large m. Explicit counterexamples with E(P^m)=0 and E(QP^m)=m!≠ 0…

Erdos and Szemeredi conjectured that every finite set of reals satisfies max(|A+A|,|AA|) ≥ |A|^2-o(1). False: there are arbitrarily large A ⊂ R, of algebraic integers in a number field of degree asymp log|A|, with max(|A+A|,|AA|) ≤ |A|^2-c…

VibeMathed records no statement for this problem. See erdosproblems.com for the original.

A collection of open problems drawn from published lists, including Cahen, Fontana, Frisch and Glaz's Open Problems in Commutative Ring Theory and Erman and Sam's survey of Boij-Soderberg theory, each proved or disproved by one automated…

For every δ > 0 and infinitely many n there is a set of n lines in the plane with no intersecting quadruple such that every subset of size at least n^4/5+δ contains three concurrent lines. This improves the bound for a dual form of a…

A problem from Fajtlowicz's Graffiti program, studied by Erdős and Staton, on the Havel-Hakimi residue of common-divisor graphs. The paper resolves the problem and extends it, determining the residue's first-order scale and its nontrivial…

Two degree inequalities for circle-valued Sobolev maps have constants that degenerate as p → 1^+ or δ → 0^+. Brezis posed the problem of sharpening them; both are now sharpened, by the same power trick with elementary estimates.

For every n≥2 the paper exhibits an n-dimensional K-polystable toric Q-Fano variety whose alpha invariant is exactly 2/2n+1, answering a question of Liu and Zhuang on whether a K-semistable example exists with alpha invariant between 1/n+1…