About polytopes of valuations on finite distributive lattices (Q1065838)
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scientific article; zbMATH DE number 3922724
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | About polytopes of valuations on finite distributive lattices |
scientific article; zbMATH DE number 3922724 |
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About polytopes of valuations on finite distributive lattices (English)
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1985
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Let L be a finite distributive lattice and V(L) the real vector space of all valuations on L. The author verifies the conjecture of \textit{L. Geissinger} [Combinatorics and computing, Proc. 3rd Caribb. Conf., Cave Hill/Barbados 1981, 125-133 (1981; Zbl 0523.06005)] that the extreme points of the convex polytope \(M(L)=\{v\in V(L):\) \(0\leq v\leq 1\}\) are precisely the 0-1 valuations.
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finite distributive lattice
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valuations
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extreme points
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convex polytope
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0.92895234
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0.90872574
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0.90569186
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