Counting antichains in finite partially ordered sets
نویسندگان
چکیده
منابع مشابه
Tripled partially ordered sets
In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.
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In their paper from 1981, Milner and Sauer conjectured that for any poset 〈P,≤〉, if cf(P,≤) = λ > cf(λ) = κ, then P must contain an antichain of size κ. We prove that for λ > cf(λ) = κ, if there exists a cardinal μ < λ such that cov(λ, μ, κ, 2) = λ, then any poset of cofinality λ contains λ antichains of size κ. The hypothesis of our theorem is very weak and is a consequence of many well-known ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1981
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90210-7