Bouquets of geometric lattices: some algebraic and topological aspects

Matroid theory is in the center of Combinatorics, Finite Geometry, Lattice theory and Combinatorial Optimization. During the last decades, extensive search was done in order 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 introduced in 1983 by Deza, Frank1 and Laurent and studied in a dozen papers (cf. [7, 11, 14, 171 and references mentioned there). The following matroidal features were extended in a satisfactory way till now: -classical axiomatizations and their equivalence (axiomatizations through flats, independent sets, circuits, rank function, closure operator) (cf. [ l l , 171) -operations and extremal theorems for perfect matroid design case (cf. [11,