منابع مشابه
Probing the Arrangement of Hyperplanes
In this paper we investigate the combinatorial complexity of an algorithm to determine the geometry and the topology related to an arrangement of hyperplanes in multi-dimensional Euclidean space from the “probing” on the arrangement. The “probing” by a flat means the operation from which we can obtain the intersection of the flat and the arrangement. For a finite set H of hyperplanes in Ed, we ...
متن کاملRich Cells in an Arrangement of Hyperplanes
A cell of an arrangement of n hyperplanes is rich if its boundary contains a piece of each hyperplane. We give an asymptotically tight upper bound on the number of rich cells, as n tends to infinity. *Supported in part by Hungarian National Science Foundation grant 1907 and 1909. ‘Supported by SERC grant 90001866. ‘Research supported by NSF grants CCR-91-22103 and OTKA-4269. LINEAR ALGEBRA AND ...
متن کاملDepth 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...
متن کاملArrangement of Hyperplanes, Ii: the Szenes Formula and Eisenstein Series
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...
متن کاملArrangement of hyperplanes I: Rational functions and Jeffrey-Kirwan residue
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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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1995
ISSN: 0166-218X
DOI: 10.1016/0166-218x(94)00082-o