If the longest chain in a partial order is of length n, then the partial order can be written as a Partition of n antichains.
https://www.cse.iitb.ac.in/~nutan/courses/cs207-12/notes/lec7.pdf
Reference for more details.
CHAIN : Let (A ,⋨) be a Poset .A subset of A is called Chain if every two elements in the subset are related.
ANTICHAIN: A subset of A is called Antichain if no two distinct elements in the subset are related.
THEOREM: Let (A ,⋨) be a Poset.Suppose the length of the longest chains in A is n.Then the elements in A can be partitioned into n disjoint Antichains.
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