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.
متن کاملMonodromy of hypergeometric functions arising from arrangements of hyperplanes
Given an arrangement of hyperplanes in P, possibly with non-normal crossings, we give a vanishing lemma for the cohomology of the sheaf of q-forms with logarithmic poles along our arrangement. We give a basis for the ideal J of relations for the Orlik-Solomon’s algebra. Under certain genericity conditions it was shown by H. Esnault, V. Schechtman and E. Viehweg that the cohomology of a local sy...
متن کاملChambers of Arrangements of Hyperplanes and Arrow’s Impossibility Theorem
Let A be a nonempty real central arrangement of hyperplanes and Ch be the set of chambers of A. Each hyperplane H defines a half-space H and the other half-space H. Let B = {+,−}. For H ∈ A, define a map ǫ H : Ch → B by ǫ H (C) = + (if C ⊆ H) and ǫ H (C) = − (if C ⊆ H). Define ǫ H = −ǫ H . Let Ch = Ch×Ch× · · · ×Ch (m times). Then the maps ǫ H induce the maps ǫ H : Ch → B. We will study the adm...
متن کاملDe Rham cohomology of logarithmic forms on arrangements of hyperplanes
The paper is devoted to computation of the cohomology of the complex of logarithmic differential forms with coefficients in rational functions whose poles are located on the union of several hyperplanes of a linear space over a field of characteristic zero. The main result asserts that for a vast class of hyperplane arrangements, including all free and generic arrangements, the cohomology algeb...
متن کاملBounding the number of k-faces in arrangements of hyperplanes
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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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1993
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02573989