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Strong properties in partially ordered sets II

✍ Scribed by Konrad Engel

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
370 KB
Volume
48
Category
Article
ISSN
0012-365X

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✦ Synopsis

An [a,/3)-normal poset with (a,/3)-logarithmic concave Whitney numbers is a normal poset with logarithmic concave Whitney numbers, with the additional condition that, without mentioning trivial cases, in the definitional inequalities for normality and logarithmic concavity equality can only hold in the exceptional intervals [a,/3) or (a,/3), respectively. A theorem is proved, where some conditions for the posets P and Q are given such that P x Q is an [a,/3)-normal poset with (a,/3)-logarithmic concave Whitney numbers. Some corollaries are deduced from which the strong h-family property of many posets can be obtained.

πŸ“œ SIMILAR VOLUMES

Strong properties in partially ordered s
Strong properties in partially ordered sets I
✍ Konrad Engel πŸ“‚ Article πŸ“… 1983 πŸ› Elsevier Science 🌐 English βš– 487 KB

Let P be a ranked partially ordered set. An h-family is a subset of P such that no h + 1 elements of the family lie on any single chain. P has the strong h-family property, if each maximal h-family in P is the union of h complete levels. Sufficient conditions for the strong h-family property are giv