Equicardinality of Bases in B-Matroids
Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 861-862
Voir la notice de l'article provenant de la source Cambridge University Press
It is very well known that any two bases of a finitary matroid (see [2] for definitions) have the same cardinality. As Dlab has shown in [1], the same does not hold for arbitrary transitive exchange spaces; indeed, since the examples Dlab constructs in [1] are matroids, it does not even hold for arbitrary matroids. Nevertheless with the aid of the generalized continuum hypothesis (G. C.H.) we are able to prove the result for B-matroids.
Higgs, Denis. Equicardinality of Bases in B-Matroids. Canadian mathematical bulletin, Tome 12 (1969) no. 6, pp. 861-862. doi: 10.4153/CMB-1969-112-6
@article{10_4153_CMB_1969_112_6,
author = {Higgs, Denis},
title = {Equicardinality of {Bases} in {B-Matroids}},
journal = {Canadian mathematical bulletin},
pages = {861--862},
year = {1969},
volume = {12},
number = {6},
doi = {10.4153/CMB-1969-112-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1969-112-6/}
}
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