Bouquets of Geometric Lattices: some Algebraic and Topological Aspects
Laurent, Monique; Deza, Michel (1989), Bouquets of Geometric Lattices: some Algebraic and Topological Aspects, Annals of Discrete Mathematics, 43, p. 279-313. http://dx.doi.org/10.1016/S0167-5060(08)70582-X
TypeArticle accepté pour publication ou publié
Journal nameAnnals of Discrete Mathematics
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Abstract (EN)This chapter discusses the bouquets of geometric lattices. Matroid theory is in the center of Combinatorics, Finite Geometry, Lattice theory and Combinatorial Optimization. During the last decades, extensive search was done to find a good degree of generality which still preserves the validity of deep results known for matroids. One of such generalizations is the concept of bouquet of matroids. Following features of bouquets are presented in the chapter: other operations (contraction, restriction and cuts), strong maps and mapping cylinders, representability, topological aspects and, in particular, shellability of various simplicial complexes associated with bouquets and relation with connectivity properties. It is suggested that Wachs and Walker principal concepts and results (strong map, mapping cylinder, realization theorem) stated for geometric semilattices could be naturally extended for the broader framework of bouquets.
Subjects / Keywordsbouquet of matroids; Matroid theory
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