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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A partial order on the regions of $ {\bf R}\sp{n}$ dissected by hyperplanes


Author: Paul H. Edelman
Journal: Trans. Amer. Math. Soc. 283 (1984), 617-631
MSC: Primary 51M20; Secondary 06A10, 52A25
MathSciNet review: 737888
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Abstract: We study a partial order on the regions of $ {{\mathbf{R}}^n}$ dissected by hyperplanes. This includes a computation of the Möbius function and, in some cases, of the homotopy type. Applications are presented to zonotopes, the weak Bruhat order on Weyl groups and acyclic orientations of graphs.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0737888-6
PII: S 0002-9947(1984)0737888-6
Article copyright: © Copyright 1984 American Mathematical Society