External and internal elements of a matroid basis. (English) Zbl 0887.05012
The problem to characterize the sets of externally and internally active elements in a matroid is considered.
Reviewer: Martin Loebl (Praha)
MSC:
| 05B35 | Combinatorial aspects of matroids and geometric lattices |
References:
| [1] | A. Björner, The homology and shellability of matroids and geometric lattice, Chapter 7 in [8].; A. Björner, The homology and shellability of matroids and geometric lattice, Chapter 7 in [8]. |
| [2] | Brylawski, T., The broken-circuit complex, Trans. Amer. Math. Soc., 234, 417-433 (1977) · Zbl 0368.05022 |
| [3] | Dawson, J. E., A construction for a family of sets and its application to matroids, (McAvaney, K. L., Combinatorial Mathematics VIII. Combinatorial Mathematics VIII, Lecture Notes in Math., vol. 884 (1981), Springer: Springer New York), 136-147 · Zbl 0519.05016 |
| [4] | G. Etienne, On the Möbius algebra of a geometric lattice, submitted.; G. Etienne, On the Möbius algebra of a geometric lattice, submitted. |
| [5] | Las Vergnas, M., A correspondence between spanning trees and orientations in graphs, (Bollobás, B., Graph Theory and Combinatorics, Proc. Conf. in honour P. Erdős (1984), Academic Press: Academic Press London), 233-238 · Zbl 0546.05033 |
| [6] | M. Las Vergnas, Bases and reorientations in oriented matroids, to appear.; M. Las Vergnas, Bases and reorientations in oriented matroids, to appear. · Zbl 1053.05023 |
| [7] | Oxley, J. G., Matroid Theory (1992), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 0784.05002 |
| [8] | (White, N., Matroid Applications (1992), Cambridge Univ. Press: Cambridge Univ. Press Cambridge) · Zbl 0742.00052 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
