A partial order on the regions of 𝑅ⁿ dissected by hyperplanes

Edelman, Paul H.

doi:10.1090/S0002-9947-1984-0737888-6

A partial order on the regions of $\textbf {R}^{n}$ dissected by hyperplanes
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by Paul H. Edelman

Trans. Amer. Math. Soc. 283 (1984), 617-631

DOI: https://doi.org/10.1090/S0002-9947-1984-0737888-6

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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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