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A Partial Order on the Regions of $R^n$ Dissected by Hyperplanes

Paul H. Edelman
Transactions of the American Mathematical Society
Vol. 283, No. 2 (Jun., 1984), pp. 617-631
DOI: 10.2307/1999150
Stable URL: http://www.jstor.org/stable/1999150
Page Count: 15
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A Partial Order on the Regions of $R^n$ Dissected by Hyperplanes
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Abstract

We study a partial order on the regions of $R^n$ dissected by hyperplanes. This includes a computation of the Mobius 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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