-matroids and Pfaffian forms.
A unified treatment of the theories of matroids with coefficients and of -matroids with coefficients.
An analogue of the Krein-Milman theorem for star-shaped sets.
The Tutte group of projective spaces.
Illumination and visibility problems in terms of closure operators.
Valuated matroids---a new look at the greedy algorithm.
On solution sets of information inequalities
We investigate solution sets of a special kind of linear inequality systems. In particular, we derive characterizations of these sets in terms of minimal solution sets. The studied inequalities emerge as information inequalities in the context of Bayesian networks. This allows to deduce structural properties of Bayesian networks, which is important within causal inference.
Hierarchical models, marginal polytopes, and linear codes
In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.
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