منابع مشابه
Complete ordered sets with no infinite antichains
There are several standard constructions by which an arbitrary ordered set P is extended to one in which every subset has an. infimum and a supremuma complete ordered set. The collection I(P) of all initial segments of P ordered by inclusion is one. [A subset I of P is an initial segment if, for x, y E P, x E I whenever x s y and y E I.] I(P) is a complete distributive lattice. AnoWr is the fam...
متن کاملOrdered sets with no infinite antichains
One approach to analyzing the structure of an ordered set has been to characterize its structure in terms of that of related objects, and vice versa. For example results in [2] characterize in terms of the ordered set P when the lattice Z(P) of lower sets (also called initial segments) of P and the ordered set Id(P) of order ideals (or simply ideals) of P have infinite antichains. The results i...
متن کاملAntichains in partially ordered sets of singular cofinality
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 ...
متن کاملLarge Infinite Antichains of Permutations
Infinite antichains of permutations have long been used to construct interesting permutation classes and counterexamples. We prove the existence and detail the construction of infinite antichains with arbitrarily large growth rates. As a consequence, we show that every proper permutation class is contained in a class with a rational generating function. While this result implies the conclusion ...
متن کاملTripled 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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1987
ISSN: 0012-365X
DOI: 10.1016/0012-365x(87)90010-0