Geodesic
Basis-transitive matroids
Journal of Algebraic Combinatorics, Tome 3 (1994) no. 3, pp. 285-290.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider the problem of classifying all finite basis-transitive matroids and reduce it to the classification of the finite basis-transitive and point-primitive simple matroids (or geometric lattices, or dimensional linear spaces). Our main result shows how a basis- and point-transitive simple matroid is decomposed into a so-called supersum. In particular each block of imprimitivity bears the structure of two closely related simple matroids, and the set of blocks of imprimitivity bears the structure of a point- and basis-transitive matroid.
Keywords: matroid, geometric lattice, dimensional linear space, transitivity, automorphism group 
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Delandtsheer, Anne; Li, Huiling. Basis-transitive matroids. Journal of Algebraic Combinatorics, Tome 3 (1994) no. 3, pp. 285-290. http://geodesic.mathdoc.fr/item/JAC_1994__3_3_a2/