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Bounding the number of k-faces in arrangements of hyperplanes

✍ Scribed by Komei Fukuda; Shigemasa Saito; Akihisa Tamura; Takeshi Tokuyama

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
829 KB
Volume
31
Category
Article
ISSN
0166-218X

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## Every arrangement %' of a&e hyperplanes in Rd determines a partition of Rd into open topological cells. The face lattice L(X) of this partition was the object of a smdy by Barnabei and Brini, wko de.;ermined the homotopy type of its intervals. We use g:am&ic con~huctions from the theory of conv

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In this paper, we compute the exact number of k-face cells of the cyclic arrangements which are the dual to the well-known cyclic polytopes. The proof uses the combinatorial interpretation of arrangements in terms of oriented matroids.