Bouquets of maroids, d-injection geometries and diagrams
F-squashed geometries, one of the many recent generalizations of matroids, include a wide range of combinatorial structures but still admit a direct extension of many matroidal axiomatization and also provide a good framework for studying the performance of the greedy algorithm in any independence system. Here, after giving all necessary preliminaries in section 1, we consider in section 2 F-squashed geometries which are exactly the shadow structures coming from the Buekenhout diagram: \(----o^{L}...----o^{L}----o^{\Pi},\) i.e. bouquets of matroids. We introduce d-injective planes: \(----o^{[d]}\) (generalizing the case of dual net for \(d=1)\) which provide a diagram representation for high rank d-injective geometries. In section 3, after a brief survey of known constructions for d-injective geometries, we give two new constructions using pointwise and setwise action of a class of mappings. The first one, using some features of permutation geometries (i.e. 2-injection geometries), produces bouquets of pairwise isomorphic matroids. The last section 4 presents briefly some related problems for squashed geometries.
bouquets of pairwise isomorphic matroids
scientific article; zbMATH DE number 4029590
scientific article