… In this paper we focus on generating isomorph-free matroids representable over GF(q). We
will focus only on generating combinatorial geometries (simple matroids) because a matroid …

… The nonembeddability result depends on our algorithm for generating oriented matroids …
The lower bound for the number of colors which are sufficient for map coloring on a surface …

… is the core of a course on combinatorics that I have given to … most stimulating seminar on the
applications of matroids in 1966. I … This is a matroid on S, called the uniform matroid of rank k …

… on matroids - in particular, what I believe to be a simplified approach to basic ideas of
Whitney and Tutte on matroid … n G, can be used as part of the generation of the like structures …

… The representations which are discussed in this thesis are based on graphs that are
defined by the oriented matroids, namely tope graphs and cocircuit graphs. The first part of this …

… theorem describing a minimal generating set for every I(ℓ); (b) … the largest degree of a minimal
algebra generator of Rs(I); (d) … –Reisner ideals of uniform matroids on some groundset [n], …

… minimal generating set of a toric ideal is a well-studied and difficult problem. In 1980 White
conjectured that the toric ideal associated to a matroid is … for strongly base orderable matroids. …

… case of the Higgins problem; it will be generalized to cover the Higgins problem. Theorem 1
… In this section we focus attention on the transversal matroid Ma=(E, F), F being the family of …

… In Section 2, we develop the necessary background on Chow rings of matroids. In Section
3, we introduce the simplicial presentation of the Chow ring, study its structural properties via …

… Special cases of these problems include the generation of … We also consider some tractable
and NP-hard generation … hyperplane enumeration problems for two matroids on S, and we …