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math.CO2026
A Characterization for Spectral and Trace Positivity of Matrix Words
Frederik Garbe, Fan Wei
In this paper, we provide a complete structural characterization of which words in noncommuting matrix variables and their formal transposes universally evaluate to matrices with n…
math.CO2026
Hamiltonicity of inhomogeneous random graphs
Frederik Garbe, Jan Hladký, Simón Piga
We provide a complete characterization of those graphons for which the inhomogeneous random graph \(\G(n,W)\) is asymptotically almost surely Hamiltonian. The characterization…