Webis that the class of geometric lattices, which is cryptomorphic to the category of simple matroids, is the same as the class of intersection lattices of arrangements of homotopy spheres. The interpretation of a geometric lattice as an arrangement of ho-motopy spheres is a natural generalization of the Folkman-Lawrence theorem. WebIt has been clear within the last ten years that combinatorial geometry, together with its order-theoretic counterpart, the geometric lattice, can serve to catalyze the whole field of combinatorial theory, and a major aim of this book, now available in a preliminary edition, is to present the theory in a form accessible to mathematicians working in disparate subjects.

Cryptomorphic structures of the lithosphere: Their reflection on space …

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Matroids - University of Texas at Austin

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