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Topological representations of matroids


Author: E. Swartz
Journal: J. Amer. Math. Soc. 16 (2003), 427-442
MSC (2000): Primary 05B35; Secondary 52C40, 13D02, 13F55
DOI: https://doi.org/10.1090/S0894-0347-02-00413-7
Published electronically: 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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Additional Information

E. Swartz
Affiliation: Malott Hall, Cornell University, Ithaca, New York 14853
Email: ebs@math.cornell.edu

DOI: https://doi.org/10.1090/S0894-0347-02-00413-7
Keywords: Matroid, geometric lattice, homotopy sphere, minimal cellular resolution
Received by editor(s): August 29, 2002
Received by editor(s) in revised form: November 4, 2002
Published electronically: November 29, 2002
Additional Notes: Partially supported by a VIGRE postdoc under NSF grant number 9983660 to Cornell University
Article copyright: © Copyright 2002 American Mathematical Society

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