Wagowski, M., Coordinatization of B-matroids, Discrete Mathematics 111 (1993) 465-479. We prove that the class of C-matroids whose circuits intersect cocircuits on finite sets is closed under the taking of minors, and we show that through the concept of matroids with coefficients it is possible to
On the coordinatization of oriented matroids
✍ Scribed by Jürgen Bokowski; Bernd Sturmfels
- Publisher
- Springer
- Year
- 1986
- Tongue
- English
- Weight
- 653 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0179-5376
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Consider a finite family of hyperplanes \_%? = {Hi, . \_. , H,} in the finite-dimensional vector space IWd. We call chambers (determined by 2) the connected components of W"\ U y=, Hi. Galleries are finite families of chambers (C,,,C,, , C,), where exactly one hyperplane separates Ci+i from Ci, for
For uniform oriented matroids M with n elements, there is in the realizable case a sharp lower bound L r (n) for the number mut(M) of mutations of M : L r (n) = n ≤ mut(M), see Shannon [17]. Finding a sharp lower bound L(n) ≤ mut(M) in the non-realizable case is an open problem for rank d ≥ 4. Las V
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