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The directions determined by n points in the plane: a matroidal generalization

✍ Scribed by Raul Cordovil

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
660 KB
Volume
43
Category
Article
ISSN
0012-365X

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✦ Synopsis

Scott posed the problem of determining the minimum number of directions determined by n points which are not all collinear in the plane. We consider a generalization of this problem for oriented marroids. We prove the following theorem: Let M denote an oriented matroid of rank 3. Suppose M has a modular line L, such that the n points of M not in L arc not all collinear. Then L has at least $( n + 3) points.

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## Abstract A boundary value problem for harmonic functions outside cuts in a plane is considered. The jump of the normal derivative is specified on the cuts as well as a linear combination of the normal derivative on one side of the cut and the jump of the unknown function. The problem is studied