4 papers
Borel dimension growth and hyperfiniteness
Jan Grebík, Andrew S. Marks, Václav Rozhoň +1
We show that every increasing union of Borel graphs of pointwise volume growth at most is hyperfinite, where is the unique real root of $(1 - γ)^3…
Bolzano: Case Studies in LLM-Assisted Mathematical Research
Martin Balko, Jan GrebÃk, Pavel HubáÄek +5
We report new results on eight problems in mathematics and theoretical computer science, produced with the assistance of Bolzano, an open-source multi-agent LLM system. Bolzano orc…
Convergence of spectra of digraph limits
Jan GrebÃk, Daniel Král', Xizhi Liu +2
The relation between densities of cycles and the spectrum of a graphon, which implies that the spectra of convergent graphons converge, fundamentally relies on the self-adjointness…
Fractional Divisibility of Spheres with Partially Generic Sets of Rotations
Jan GrebÃk, Christian Ikenmeyer, Oleg Pikhurko
We say that an r-tuple of special orthogonal matrices fractionally divides the -dimensional sphere if there is a non-constant function in $L^…