A generalisation of uniform matroids

Uniform Families and Count Matroids

On series-parallel extensions of uniform matroids

This paper gives an excluded-minor characterization of the class of matroids that are series-parallel extensions of uniform matroids.

Total Polynomials of Uniform Oriented Matroids

In this paper we introduce polynomials associated with uniform oriented matroids whose coefficients enumerate cells in the corresponding arrangements. These polynomials are quite useful in the study of many enumeration problems of combinatorial geometry, such as counting faces of polytopes, counting Radon partitions, counting k-sets, and so forth. We also describe some striking equations relati...

A characterization of cocircuit graphs of uniform oriented matroids

The cocircuit graph of an oriented matroid is the 1-skeleton of the cellular decomposition induced by the Topological Representation Theorem due to Folkman and Lawrence (1978) [J. Folkman, J. Lawrence, Oriented matroids, J. Combin. Theory Ser. B 25 (1978) 199–236]. In this paper we exhibit a characterization of such graphs (for the uniform case) via their natural embedding into Qn—the 1-skeleto...

Cubic time recognition of cocircuit graphs of uniform oriented matroids

We present an algorithm which takes a graph as input and decides in cubic time if the graph is the cocircuit graph of a uniform oriented matroid. In the affirmative case the algorithm returns the set of signed cocircuits of the oriented matroid. This improves an algorithm proposed by Babson, Finschi and Fukuda. Moreover we strengthen a result of Montellano-Ballesteros and Strausz about crabbed ...