EMIS ELibM Electronic Journals Journal of Applied Analysis
Vol. 1, No. 1, pp. 1-11 (1995)

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Minimal fixing systems for convex bodies

V.G. Boltyanski and E. Morales Amaya

V. G. Boltyanski
Steklov Mathematical Institute
of Russian Academy of Sciences
Vavilov-str. 42, Moscow 117966
E. Morales Amaya
Centro de Investigationes
en Mathematicas, A.P. 402
36000 Guanajuato, GTO

Abstract: L. Fejes Tóth [1] introduced the notion of {\it fixing system} for a compact, convex body $\, M\subset R^n.\, $ Such a system $\, F\subset \bd \, M\, $ stabilizes $\, M\, $ with respect to translations. In particular, every {\it minimal} fixing system $\, F\, $ is {\it primitive}, i.e., no proper subset of $\, F\, $ is a fixing system. In [2] lower and upper bounds for cardinalities of mimimal fixing systems are indicated. Here we give an improved lower bound and show by examples, now both the bounds are exact. Finally, we formulate a {\it Fejes Tóth Problem.}

Keywords: Convex body, fixing system, illumination, minimal dependency, functional $md$, indecomposable bodies, combinational geometry

Classification (MSC2000): 52A20, 52A37, 52B05

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Electronic fulltext finalized on: 28 May 2002. This page was last modified: 21 Dec 2002.

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