ARRANGEMENTS OF HYPERPLANES IN ℝ3AND THEIR FREENESS
نویسندگان
چکیده
منابع مشابه
Inductively Factored Signed-graphic Arrangements of Hyperplanes
In 1994, Edelman and Reiner characterized free and supersolvable hyperplane arrangements in the restricted interval [An−1, Bn]. In this paper, we give a characterization of inductively factored arrangements in this interval, and show that the same characterization also describes factored arrangements in this interval. These results use the compact notation of signed graphs introduced by Zaslavsky.
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Generalizing a result of Yoshinaga in dimension 3, we show that a central hyperplane arrangement in 4-space is free exactly if its restriction with multiplicities to a fixed hyperplane of the arrangement is free and its reduced characteristic polynomial equals the characteristic polynomial of this restriction. We show that the same statement holds true in any dimension when imposing certain tam...
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Let G be a simple graph on the vertex set {v1, . . . , vn} with edge set E. Let K be a field. The graphical arrangement AG in K n is the arrangement xi − xj = 0, vivj ∈ E. An arrangement A is supersolvable if the intersection lattice L(c(A)) of the cone c(A) contains a maximal chain of modular elements. The second author has shown that a graphical arrangement AG is supersolvable if and only if ...
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Fukuda, K., S. Saito, A. Tamura and T. Tokuyama, Bounding the number of k-faces in arrangements of hyperplanes, Discrete Applied Mathematics 31 (1991) 151-165. We study certain structural problems of arrangements of hyperplanes in d-dimensional Euclidean space. Of special interest are nontrivial relations satisfied by the f-vector f = Lfo, fi, . , fd) of an arrangement, where fk denotes the num...
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We show that, for any collection H of n hyperplanes in < 4 , the combinato-rial complexity of the vertical decomposition of the arrangement A(H) of H is O(n 4 log n). The proof relies on properties of superimposed convex subdivisions of 3-space, and we also derive some other results concerning them.
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ژورنال
عنوان ژورنال: Honam Mathematical Journal
سال: 2009
ISSN: 1225-293X
DOI: 10.5831/hmj.2009.31.1.025