Line-closed combinatorial geometries (Q1088668)
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scientific article; zbMATH DE number 3991520
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Line-closed combinatorial geometries |
scientific article; zbMATH DE number 3991520 |
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Line-closed combinatorial geometries (English)
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1987
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We present some results on combinatorial geometries (geometric lattices) in which closure is line-closure. We prove that every interval of a line- closed geometry is line-closed. Furthermore, if every rank 3 interval of a geometry is line-closed, then the geometry is line-closed. This implies that every supersolvable geometry is line-closed. Though not true in general, supersolvability does characterize the line-closed graphic geometries.
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combinatorial geometries
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geometric lattices
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