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Depth in an Arrangement of Hyperplanes

โœ Scribed by P. J. Rousseeuw; M. Hubert

Publisher
Springer
Year
1999
Tongue
English
Weight
129 KB
Volume
22
Category
Article
ISSN
0179-5376

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๐Ÿ“œ SIMILAR VOLUMES

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Let ~ be an arrangement of n hyperplanes in pa, C(,~ยขt~) its cell complex, and Hany hyperplane of~Ze. It is proved: (I) If~ is not a near pencil then there are at least n -d -I simplicial d-cells of C(,,~), each having no facet in H. (2) There are at least d + I simplicial d-cells of C(~ยขt~), each h

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We investigate several hyperplane arrangements that can be viewed as deformations of Coxeter arrangements. In particular, we prove a conjecture of Linial and Stanley that the number of regions of the arrangement x i &x j =1, 1 i< j n, is equal to the number of alternating trees on n+1 vertices. Rema

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We show in this paper that the projective d-arrangement I$ a formed by the facet hyperplanes of a cross-polytope, its hyperplanes of mirror symmetry, and the hyperplane at infinity is simplicial precisely for d ~< 4. The arrangement 1$ 4 is the only simplicial d-arrangement presently known that doe