On modular pairs in posets. (Q2925282)
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scientific article; zbMATH DE number 6359482
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On modular pairs in posets. |
scientific article; zbMATH DE number 6359482 |
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21 October 2014
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modular pairs
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M-symmetry
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posets
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covering properties
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forbidden configurations
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0.8759051
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On modular pairs in posets. (English)
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The concept of a modular pair in lattices is well-known and studied for years. Garrett Birkhoff posed the problem of how to define modular pairs in posets. Several definitions were already introduced by various authors. The present authors introduced a new concept of a modular pair defined in terms of maximal elements of the lower cone and minimal elements of the upper cone. The relation between this definition and existing ones is studied for different classes of posets. In fact, for lattices both of these concepts coincide. There are presented several characterizations of modular pairs in atomistic and semi-orthogonal posets.
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