✦ LIBER ✦

Covering posets

✍ Scribed by Gerhard Behrendt

Publisher: Elsevier Science
Year: 1988
Tongue: English
Weight: 811 KB
Volume: 71
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90099-4

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✦ Synopsis

A pair (a, b) of elements of a partially ordered set (X, G) is called a covering pair if a C b and whenever x E X is such that n sx s b then x E {a, b}. The set C(X) of covering pairs can be partially ordered by (ea, b) S (a', b') if and only if (a, b) = (a', b') or b Sa'. The pose! ) is called the covering poset of (X, G). We give neassary and sufkient conditions for a poset to be isomorphic to the covering poset of a finite poset. We describe some relations between finite posets which have isomorphic covering posets, and we consider the dimension and other parameters of covering posets.

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