**Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 283-289 (1999)
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The Largest Intersection Lattice of a Discriminantal Arrangement

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Christos A. Athanasiadis

Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104-6395, USA, email: athana@math.upenn.edu

**Abstract:** We prove a conjecture of Bayer and Brandt [J. Alg. Combin.** 6** (1997), 229-246] about the "largest" intersection lattice of a discriminantal arrangement based on an essential arrangement of $n$ linear hyperplanes in $\hbox** R**^k$. An important ingredient in the proof is Crapo's characterization of the matroid of circuits of the configuration of $n$ generic points in $** R**^k$.

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