Characterizations of transversal and fundamental transversal matroids.
Circuit and cocircuit partitions of binary matroids
We give an example of a class of binary matroids with a cocircuit partition and we give some characteristics of a set of cocircuits of such binary matroids which forms a partition of the ground set.
Combinatorial Models for the Finite-Dimensional Grassmannians.
Combinatorial Obstructions to the Lifting of Weaving Diagrams.
Connectivity of the lifts of a greedoid.
Construction methods for gaussoids
The number of -gaussoids is shown to be a double exponential function in . The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing -minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed -minors.
Contribution of František Matúš to the research on conditional independence
An overview is given of results achieved by F. Matúš on probabilistic conditional independence (CI). First, his axiomatic characterizations of stochastic functional dependence and unconditional independence are recalled. Then his elegant proof of discrete probabilistic representability of a matroid based on its linear representability over a finite field is recalled. It is explained that this result was a basis of his methodology for constructing a probabilistic representation of a given abstract...
Correspondence between two antimatroid algorithmic characterizations.
Counting simplexes in .
Cycle index, weight enumerator, and Tutte polynomial.