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ISSN 1088-6834(e) ISSN 0894-0347(p)

Topological representations of matroids

Author(s): E. Swartz
Journal: J. Amer. Math. Soc. 16 (2003), 427-442.
MSC (2000): Primary 05B35; Secondary 52C40, 13D02, 13F55
Posted: November 29, 2002
MathSciNet review: 1949166
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Abstract: There is a one-to-one correspondence between geometric lattices and the intersection lattices of arrangements of homotopy spheres. When the arrangements are essential and fully partitioned, Zaslavsky's enumeration of the cells of the arrangement still holds. Bounded subcomplexes of an arrangement of homotopy spheres correspond to minimal cellular resolutions of the dual matroid Steiner ideal. As a result, the Betti numbers of the ideal are computed and seen to be equivalent to Stanley's formula in the special case of face ideals of independence complexes of matroids.

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