Bouquets of maroids, d-injection geometries and diagrams
type: Item
instance of: scholarly article
title: Bouquets of maroids, d-injection geometries and diagrams
zbMATH Open document ID: 0633.05020
DOI: 10.1007/BF01234984
author: Monique Laurent
author: Michel Deza
published in: Journal of Geometry
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05B99
Mathematics Subject Classification ID: 51E99
zbMATH DE Number: 4029590
zbMATH Keywords: F-squashed geometries
zbMATH Keywords: matroids
zbMATH Keywords: greedy algorithm
zbMATH Keywords: Buekenhout diagram
zbMATH Keywords: d- injective planes
zbMATH Keywords: d-injective geometries
zbMATH Keywords: bouquets of pairwise isomorphic matroids
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4029590