منابع مشابه
Depth in an Arrangement of Hyperplanes
Peter J. Rousseeuw and Mia Hubert Revised version, 25 May 1998 Department of Mathematics and Computer Science, U.I.A., Universiteitsplein 1, B-2610 Antwerp, Belgium [email protected] Abstract A collection of n hyperplanes in Rd forms a hyperplane arrangement. The depth of a point 2 Rd is the smallest number of hyperplanes crossed by any ray emanating from . For d = 2 we prove that th...
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Consider the space R∆ of rational functions of r variables with poles on an arrangement of hyperplanes ∆. It is important to study the decomposition of the space R∆ under the action of the ring of differential operators with constant coefficients. In the one variable case, a rational function of z with poles at most on z = 0 is written uniquely as φ(z) = Princ(φ)(z)+ψ(z) where Princ(φ)(z) = ∑ n...
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A motivation for computing such sums comes from the work of E. Witten [4]. In the special case where αj are the positive roots of a compact connected Lie group G, each of these roots being repeated with multiplicity 2g − 2, Witten expressed the symplectic volume of the space of homomorphisms of the fundamental group of a Riemann surface of genus g into G, in terms of these sums. In [2], L. Jeff...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1999
ISSN: 0179-5376
DOI: 10.1007/pl00009452