4 papers
Measurable Matroids: Foundations and Min--Max Theorems
Kristóf Bérczi, András Imolay, Ádám Schweitzer
We develop a measure-theoretic analogue of matroid theory on standard atomless measure spaces. Motivated by the quotient-convergence framework for submodular set functions, our aim…
Convergent sequences of combinatorial submodular setfunctions
Kristóf Bérczi, Márton Borbényi, László Lovász +1
To illustrate that the notion of convergence of submodular function sequences fits reasonably into the limit theory of graphs, we describe several classes of matroids and other sub…
Interaction between skew-representability, tensor products, extension properties, and rank inequalities
Kristóf Bérczi, Boglárka Gehér, András Imolay +3
Skew-representable matroids form a fundamental class in matroid theory, bridging combinatorics and linear algebra. They play an important role in areas such as coding theory, optim…
Subset-Constrained Inverse Matroid Optimization
Kristóf Bérczi, Mirabel Mendoza-Cadena, José Soto
In inverse optimization, the goal is to find a minimum perturbation of weights that makes a prescribed feasible solution optimal. For matroids, the classical inverse problem fixes…