Problems
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Wellman and Pettie noted that the true leading constant for large-order Davenport-Schinzel sequences was known only to lie in an interval. The paper improves the Roselle-Stanton lower bound to match the pigeonhole upper bound in the…
Do the one-species current marginals of type-D ASEP have the predicted Tracy-Widom long-time asymptotics despite the model's two-species interactions?
Pełczyński's duality between strictly singular and strictly cosingular operators fails without weak compactness. Beanland asked, in work with Androulakis and later on MathOverflow, for the separable-range case: the paper answers it…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Among d+1 equiprobable equal-energy signals in Gaussian noise, is the regular simplex optimal for average error probability? Yes. The underlying comparison is that for any m × m correlation matrix R with R - 11^ T/m succeq 0 and X ~…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Can the minimum edge-outerplanarity of a finite loopless planar graph, minimized over all planar embeddings, be computed in polynomial time? Asked by Bentz in 2009.
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
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…
For a finite connected graph G, let L_s(G) be the maximum number of leaves in a spanning tree and ℓ(G) the average local independence number. Must L_s(G) ≥ 2(ℓ(G) - 1)?
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…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
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…
VibeMathed records no statement for this problem. See erdosproblems.com for the original.
Does the conjectured universal formula for normalized alternating syzygy power sums of numerical semigroup rings hold for every index?