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problems
Regts and Sevenster conjectured that a complex-valued graph parameter f with f(∅)=1 has exponentially bounded edge-connection rank precisely when it is a mixed partition function. The paper proves it, with the numbers of even and odd…
Let D_q(n) be the largest possible least degree of a polynomial omitted by a non-covering family of n distinct-modulus congruence classes in F_q[x]. What is its asymptotic size? The answer is D_q(n) = n/q-1 + O_q(1).
What is the best deterministic polynomial-time approximation ratio for the permanent of a Hermitian positive semidefinite matrix? Resolved up to lower-order terms in the exponent: an explicit concave maximisation widehat P(A) satisfies…
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.
Does a general pencil of plane cubics over C have exactly 12 common flex lines? Ciliberto, Miranda and Roé asked this in Remark 5.3 of their paper; the answer is yes.
Amdeberhan, Shareshian and Stanley showed a function from the theory of partition Eisenstein series counts alternating permutations with a given record partition, and asked whether a similar theory exists for record compositions,…
Two free ergodic measure-preserving flows whose L^1 full groups are isomorphic as abstract groups are conjugate up to a scalar time change. This proves the flow analogue of Belinskaya's theorem, answering a question posed by François Le…
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 fixed d, can every d-dimensional feasible solution of the triangle-strengthened Max-Cut SDP be rounded in polynomial time with ratio strictly larger than α_GW? A rounding achieving α_GW + 2^-O(d) answers yes.
A precise asymptotic formula for the number of n × 4t partial Hadamard matrices in the regimes t/n^3 → ∞ and t/n^3 → Θ, reaching the cubic regime that previous approaches (de Launey-Levin and successors) could not.
Two open problems about extracting order from trees in real-valued functions. A quantitative function analogue of Hodges's tree-to-order extraction yields an at most double-exponential bound on dual sequential fat-shattering dimension,…
Is the exact nonreal spectral region of the four-cycle family of row-stochastic nonnegative matrices determined by the Karpelevich constraint, as Ran and Teng conjectured in 2024?
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Douglas and Yang attach to each nonzero vector x of a quasinilpotent operator T a local resolvent-growth exponent k_x, giving the power set Λ(T) = k_x : x ≠ 0. Ji and Zhang asked whether 1 always belongs to Λ(T). It does, for every…
Cornulier asked, in a MathOverflow discussion, whether amenability of a module over an associative algebra depends on the ground field. It does not: the notion is invariant under change of base field.
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?
Aluffi, Chen and Marcolli conjectured that the Poincare polynomial of the Deligne-Mumford moduli space overlineM_0,n of stable n-pointed rational curves has only real roots. True, with simple roots and strict interlacing between…
Can one construct a plain-model, efficient, information-theoretically secure one-time unclonable-encryption scheme for one classical bit with exponentially small adversarial advantage?
Maz'ya and Shaposhnikova introduced a non-classical maximal operator M^diamond, the maximal convolution with the vector-valued signum kernel truncated to centered balls. One of Maz'ya's 75 open problems in analysis asks whether it can be…
For the adjacent-transposition chain on S_n with a regular parameter vector, Fill's spectral gap conjecture (recently resolved) leaves open the characterization of the equality cases. The paper settles them, constructing the additional…