Helly property in finite set systems (Q1208035)
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scientific article; zbMATH DE number 165747
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Helly property in finite set systems |
scientific article; zbMATH DE number 165747 |
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Helly property in finite set systems (English)
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16 May 1993
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This paper investigates the combinatorial counterparts of the famous Helly theorem: a finite set system satisfies the \(d\)-dimensional Helly property if every subsystem with empty intersection has a sub-subsystem of at most \(d+1\) elements with an empty intersection, again. Numerous extremal properties of \(d\)-dimensional Helly systems are proven including LYM-type inequalities. The results generalize several former theorems of B. Bollobás and P. Duchet. More open problems are formulated including a ``full'' LYM-type inequality.
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Bollobas inequality
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Sperner
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convex hull
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Helly theorem
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finite set system
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Helly property
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LYM-type inequality
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0.87411606
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0.8734317
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0.8660191
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0.86186934
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0.85860837
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