4 papers
Sharp Asymptotics for Abelian Covers of Groups with Bounded Noncommutativity
Guillaume Lecomte
We determine the sharp exponential growth rate of the minimum number of abelian subgroups required to cover a group with bounded pairwise noncommutativity. Let denote the la…
Connected Counterexamples for Target Ramsey Numbers
Guillaume Lecomte
Chartrand and Zhang asked whether there exists a graph without isolated vertices whose target Ramsey number satisfies . We answer the question a…
The Certification Limits of KS-Type Layer Relaxations: A Square-Root Ceiling and Its Breakdown
Guillaume Lecomte
A separable bilinear layer relaxation assigns a population cost to each layer and a nonpositive bilinear coupling to each pair of layers, then excludes a profile span whenever the…
A certified refinement and asymptotic analysis of the Kuznetsov-Sahinidis diameter bound for Lennard-Jones clusters
Guillaume Lecomte
Kuznetsov and Sahinidis (J. Glob. Optim., 2025) prove distance bounds that confine optimal Lennard-Jones clusters and shrink the search region of deterministic solvers; their diame…