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 | References | Similar Articles | Additional Information

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