A bound on local minima of arrangements that implies the upper bound theorem (Q1312194)
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scientific article; zbMATH DE number 488285
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bound on local minima of arrangements that implies the upper bound theorem |
scientific article; zbMATH DE number 488285 |
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A bound on local minima of arrangements that implies the upper bound theorem (English)
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19 January 1994
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The \(i\)-level of a simple arrangement of hyperplanes in \(E^ d\) is the boundary of the set of all points that are below at most \(i\) hyperplanes. Author proves an upper bound for the number of local minima of the \(i\)- level. From this he deduces by linear programming duality the Upper Bound Theorem for convex polytopes.
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dual linear program
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upper bound theorem
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arrangement of hyperplanes
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convex polytopes
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