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problems
Gao, Huo and Ma asked whether for every fixed k ≥ 3 there is a function f_k(n) → ∞ such that every n-vertex (k+1)-critical graph contains f_k(n) consecutive cycle lengths. The paper settles this and two related problems on cycle lengths…
Dogon, Levit and Vigdorovich asked for an explicit upper bound on the stability radius of an infinitely presented group. The lamplighter group provides the first: explicit polynomial bounds on both its Hilbert-Schmidt stability rate and…
If a subgroup of a product of groups of type F_k virtually surjects onto every k-tuple of factors, must it be of type F_k itself? Yes, for discrete groups, and likewise for FP_k. The homological n-(n+1)-(n+2) Conjecture follows for…
Is a Werner state that is not one-copy distillable ever two-copy distillable? The first open rung of the NPT bound-entanglement ladder, open since 2000.
Davis, Figiel, Johnson and Pełczyński showed their interpolation space admits a Schauder basis when the range space has a shrinking one. Can the DFJP space always be chosen with a basis whenever the range space has a basis? The paper…
If G is connected, cubic and diamond-free, must the zero-forcing number satisfy Z(G) ≤ γ(G) + 2? A connected cubic triangle-free 14-vertex graph has Z = 7 and γ = 4.
The Elton–Odell theorem gives, in every infinite-dimensional normed space, a unit-sphere sequence with mutual distances at least 1+ε. Over C, identifying vectors differing by a unimodular scalar gives a toroidal distance. Does every…
The discrete-time Kac walk on S^n-1 started from a coordinate vector exhibits total variation cutoff at C_BRW n log n, where C_BRW ≈ 3.8916 is set by the speed of the leftmost particle in a branching random walk. The cutoff is therefore…
Furthest Pair and its relatives admit f(d) n^2-Θ(1/d) algorithms, making them the standard examples of barely subquadratic computation, and whether that is optimal in superconstant dimension was open. Under SETH it is: Furthest Pair…
Connes' rigidity conjecture asks whether an ICC group with Kazhdan's property (T) is determined by its group von Neumann algebra. Disproved for this class: two explicit countable discrete groups Γ_1 and Γ_2, both ICC and property (T), are…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Must every r-differential poset have at least as many elements in each rank as Y^r, the r-th Cartesian power of Young's lattice? For r = 3 the new construction has fourth-rank size 50 against 51 for Y^3.
We prove a Nakai-Moishezon-type criterion for complex Hessian-type equations on projective manifolds whose associated degree-n polynomials are strongly strictly right-Noetherian. For strictly right-Noetherian polynomials of arbitrary…
Bajpai, Dona and Nitsche left three degree-six symplectic hypergeometric monodromy groups unclassified as arithmetic or thin. Two of the three, C-47 and C-55, are arithmetic.
On the basis of experiments up to 5000 nodes, Papamanthou and Tollis conjectured a relation between the longest paths produced by their MaxSTN and MinSTN algorithms for st-orientations of biconnected graphs. A counterexample refutes it.
Let x_n = tan(∑_k=1^n arctan k). Amdeberhan, Medina and Moll conjectured that x_n ∉ Z for every n ≥ 5. Any integer value x_n = m must satisfy |m| ≥ e^(1/2+o(1)) n log n, which forces #1 ≤ n ≤ N : x_n ∈ Z = O(log N). The conjecture…
At the conjectured density, must every k-uniform hypergraph contain a short nontrivial even cover - a set of hyperedges covering each vertex an even number of times - with no superfluous polylogarithmic factors? Known up to polylog factors…
The paper gives counterexamples in dimensions eight and nine to two problems: the Cartesian-product problem posed by Cassels for critical determinants and formulated by Zong for lattice packings, and a question raised by Sarnak, formulated…
Does two-terminal reliability, the probability that s still reaches t when edges fail independently, admit a fully polynomial-time randomised approximation scheme? Asked explicitly in Kannan's 1994 survey and left open while the…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.