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problems
Among sufficiently large one-separated planar point sets, does the triangular lattice maximize the number of distances below each threshold? Explicit rational oblique lattices beat the triangular lattice under several closed- and…
Must every graph with n vertices and δ n^2 edges contain large subgraphs in which every two edges lie on specified short cycles? A dense high-girth construction refutes the statement when δ may shrink with n.
Does the Dinitz-Garg-Goemans cost-preserving unsplittable-flow rounding conjecture survive on acyclic planar instances with only four terminals? An explicit instance answers no: every cost-nonincreasing unsplittable routing has upper…
For the released four-terminal planar acyclic single-source unsplittable-flow gadget, require one unsplittable routing to be no more expensive than a prescribed fractional routing under each of m strictly positive full-demand…
Does there exist a single real-valued, divergence-free, time-independent Lipschitz velocity field u∈ W^1,∞( T^3; R^3), chosen independently of magnetic diffusivity, that is a fast dynamo for the kinematic induction equation on the flat…
For every connected graph, is the deviation of its adjacency eigenvalues at most its order divided by its average distance? Exact lollipop-graph certificates refute the inequality when deviation means population standard deviation, under…
Let A⊂N be infinite. Must there exist some k≥ 1 such that almost all integers have a divisor of the form a+k for some a∈ A? The question as posed follows negatively from Davenport–Erdős (1951). The AI result settles Tenenbaum's harder…
If n planar points have no four concyclic, must some point determine (1 - o(1))n distinct distances? Failing that, can one always force more than (1/3 + c)n?
The paper proves a closed-string remodeling statement for the affine binary dihedral Calabi–Yau orbifold threefold, a target outside the toric setting of the Bouchard–Klemm–Mariño–Pasquetti remodeling conjecture, replacing the toric mirror…