Forbidden (0, 1)-vectors in hyperplanes of \(\mathbb{R}^n\): The restricted case (Q1404309)
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scientific article; zbMATH DE number 1968853
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Forbidden (0, 1)-vectors in hyperplanes of \(\mathbb{R}^n\): The restricted case |
scientific article; zbMATH DE number 1968853 |
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Forbidden (0, 1)-vectors in hyperplanes of \(\mathbb{R}^n\): The restricted case (English)
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21 August 2003
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Denote \(E(n,k)\) the set of all \((0,1)\)-vectors in \(\mathbb{R}^n\) with exactly \(k\) ones. This paper tries to determine the maximum cardinality \(F(n,m,w)\) of \(X \subset E(n,m)\) such that the span \(\langle X\rangle\) does not contain any \((0,1)\)-vector with exactly \(w\) ones. The proofs use classical extremal set theoretical results, lengthy case analysis and calculations.
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combinatorial extremal theory
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\((0, 1)\)-vectors
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dimension constraint
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forbidden weights
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nontrivial intersecting systems
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