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
On sign-invariance graphs of uniform oriented matroids
β Scribed by Raul Cordovil; Pierre Duchet
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 453 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let K be a connected and undirected graph, and M be the polygon matroid of K . Assume that, for some k 2 1, the matroid M is kseparable and k-connected according to the matroid separability and connectivity definitions of W. T. Tutte. In this paper we classify the matroid kseparations of M in terms
## Abstract A homomorphism from an oriented graph __G__ to an oriented graph __H__ is a mapping $\varphi$ from the set of vertices of __G__ to the set of vertices of __H__ such that $\buildrel {\longrightarrow}\over {\varphi (u) \varphi (v)}$ is an arc in __H__ whenever $\buildrel {\longrightarrow}
An element e of a 3-connected matroid M is essential if neither the deletion M\e nor the contraction M/e is 3-connected. Tutte's Wheels and Whirls Theorem proves that the only 3-connected matroids in which every element is essential are the wheels and whirls. In this paper, we consider those 3-conne
The connectivity of a graph G and the corank of a matroid M are denoted by K(G) and p, respectively. X is shown that if a graph G is the base graph of a simple mat&d M, then K(G) L 2p and the lower bound of 2p izA best possible.