Let M and N be ternary matroids having the same rank and the same ground set, and assume that every independent set in N is also independent in M. The main result of this paper proves that if M is 3-connected and N is connected and non-binary, then M = N . A related result characterizes precisely wh
Representing Weak Maps of Oriented Matroids
β Scribed by Laura Anderson
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 109 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0195-6698
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π SIMILAR VOLUMES
Let F be a field and let N be a matroid in a class N N of F-representable matroids that is closed under minors and the taking of duals. Then N is an F-stabilizer for N N if every representation of a 3-connected member of N N is determined up to elementary row operations and column scaling by a repre
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
We obtain an explicit method to compute the cd-index of the lattice of regions of an oriented matroid from the ab-index of the corresponding lattice of flats. Since the cd-index of the lattice of regions is a polynomial in the ring Z( c, 2d), we call it the c-2d-index. As an application we obtain a
A matroid or oriented matroid is dyadic if it has a rational representation with all nonzero subdeterminants in [ \2 k : k # Z]. Our main theorem is that an oriented matroid is dyadic if and only if the underlying matroid is ternary. A consequence of our theorem is the recent result of G. Whittle th