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math.CO2026
Many rays of the submodular cone
Georg Loho, Arnau Padrol, Germain Poullot
The study of the cone of submodular functions goes back to Jack Edmonds' seminal 1970 paper, which already highlighted the difficulty of characterizing its extreme rays. Since then…
math.CO2025
Quotients of M-convex sets and M-convex functions
Marie-Charlotte Brandenburg, Georg Loho, Ben Smith
We unify the study of quotients of matroids, polymatroids, valuated matroids and strong maps of submodular functions in the framework of Murota's discrete convex analysis. As a mai…
math.CO2024
The Real Tropical Geometry of Neural Networks
Marie-Charlotte Brandenburg, Georg Loho, Guido Montúfar
We consider a binary classifier defined as the sign of a tropical rational function, that is, as the difference of two convex piecewise linear functions. The parameter space of ReL…