An inequality in binary vector spaces (Q1079808)
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scientific article; zbMATH DE number 3964851
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An inequality in binary vector spaces |
scientific article; zbMATH DE number 3964851 |
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An inequality in binary vector spaces (English)
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1986
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The author considers the following problem posed by Ganter: ''Let V be a vector space over GF(2) such that \[ V =\cup^{k}_{i=1}U_ i;\quad V \neq \cup_{1\leq i\leq k, i\neq j}U_ i\quad (j=1,...,k);\quad \cap^{k}_{i=1}U_ i= \emptyset. \] Does this imply that dim V\(<k ?''\) and gives an affirmative answer. This settles a conjecture by G. Bruns on the covering of Boolean algebra by subalgebras.
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n-dimensional vector space over GF(2)
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union of subspaces
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problem of Ganter
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conjecture of Bruns
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covering of Boolean algebra by subalgebras
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