A counterexample to Valette's conjecture (Q741185)
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scientific article; zbMATH DE number 6342484
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A counterexample to Valette's conjecture |
scientific article; zbMATH DE number 6342484 |
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A counterexample to Valette's conjecture (English)
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10 September 2014
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The author constructs a simple 4-dimensional counterexample to the following \textit{Conjecture 1.} Let \( K\) be a self-affine body in \({\mathbb R}^d \), \( d \geq 2 \); then \( K \) is either a polytope or affinely equivalent to a product of a convex body with a polytope of lower positive dimension. Some additional assumptions which make this Conjecture true are formulated as well as \textit{Problem 1.} Is the Conjecture \(1\) true for \( d = 3 \)?
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self-affine convex bodies
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self-affine partition
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refinable self-affine partition
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