The number of small covers over cubes

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In the present paper we find a bijection between the set of small covers over an n-cube and the set of acyclic digraphs with n labeled nodes. Using this, we give formulas of the number of small covers over an n-cube (generally, a product of simplices) up to Davis-Januszkiewicz equivalence classes and Z(2)(n)-equivariant homeomorphism classes. Moreover we prove that the number of acyclic digraphs with n unlabeled nodes is an upper bound of the number of small covers over an n-cube up to homeomorphism.
Publisher
GEOMETRY TOPOLOGY PUBLICATIONS
Issue Date
2008
Language
English
Article Type
Article
Citation

ALGEBRAIC AND GEOMETRIC TOPOLOGY, v.8, no.4, pp.2391 - 2399

ISSN
1472-2739
URI
http://hdl.handle.net/10203/227524
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