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math.CO2024
Matroid products via submodular coupling
Kristóf Bérczi, Boglárka Gehér, András Imolay +3
The study of matroid products traces back to the 1970s, when Lovász and Mason studied the existence of various types of matroid products with different strengths. Among these, the…
math.CO2024
Monotonic Decompositions of Submodular Set Functions
Kristóf Bérczi, Boglárka Gehér, András Imolay +2
Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions ha…
cs.DM2024
Problems on Group-labeled Matroid Bases
Florian Hörsch, András Imolay, Ryuhei Mizutani +2
Consider a matroid equipped with a labeling of its ground set to an abelian group. We define the label of a subset of the ground set as the sum of the labels of its elements. We st…