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The illumination conjecture and its extensions |
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| Authors: | Károly Bezdek |
| Institution: | 2101. Department of Mathematics and Statistics, University of Calgary & Department of Geometry E?tv?s Loránd University, 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada & Pázmány Péter sétány 1/c H-1117 Budapest, Hungary |
| Abstract: | Summary The Illumination Conjecture was raised independently by Boltyanski and Hadwiger in 1960. According to this conjecture any <InlineEquation ID=IE"1"><EquationSource Format="TEX"><!CDATA<InlineEquation ID=IE"2"><EquationSource Format="TEX"><!CDATA<InlineEquation ID=IE"3"><EquationSource Format="TEX"><!CDATA$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>d$-dimensional convex body can be illuminated by at most $2^d$ light sources. This is an important fundamental problem. The paper surveys the state of the art of the Illumination Conjecture. |
| Keywords: | covering by homothets illumination by affine subspaces |
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