Answer by Sarvesh Ravichandran Iyer for Relation between sizes of chains and...
(We are assuming that $\frac nc$ is an integer, but you can see everything going through with slight modification if it were not).Let $P$ be a poset with $n$ elements, and $c$ be the size of the...
View ArticleAnswer by Angina Seng for Relation between sizes of chains and antichains in...
Suppose there's no chain of size $>c$. Then in every decomposition of $P$into disjoint chains, there are at least $n/c$ chains. Now by Dilworth's theorem,the size of the largest antichain is the...
View ArticleRelation between sizes of chains and antichains in a poset
The questions is to,Show that every partially ordered set with $n$ elements either contains a chains of size greater than $c$ or an anti-chain of size at least $n/c$.I only know definitions of chains...
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