An Orlik-Solomon type algebra for matroids with a fixed linear class of circuits.
Applications of combinatorics to statics – a survey
Bases of certain finite groups
Bergman complexes, Coxeter arrangements, and graph associahedra.
Binomial residues
A binomial residue is a rational function defined by a hypergeometric integral whose kernel is singular along binomial divisors. Binomial residues provide an integral representation for rational solutions of -hypergeometric systems of Lawrence type. The space of binomial residues of a given degree, modulo those which are polynomial in some variable, has dimension equal to the Euler characteristic of the matroid associated with .
Bipartite graphs that are not circle graphs
The following result is proved: if a bipartite graph is not a circle graph, then its complement is not a circle graph. The proof uses Naji’s characterization of circle graphs by means of a linear system of equations with unknowns in .At the end of this short note I briefly recall the work of François Jaeger on circle graphs.
Broken Circuits in Matroids-Dohmen’s Inductive Proof
Dohmen [4] gives a simple inductive proof of Whitney’s famous broken circuits theorem. We generalise his inductive proof to the case of matroids
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.
Diagonal similarity of matrices
Discrete polymatroids.
Dualities in signed vector systems