Dilworth's theorem

Dilworth's Theorem is a principle in order theory that states in any finite partially ordered set, you can divide the set into the smallest number of chains (where every element is comparable) such that every element can belong to exactly one chain. This number is equal to the size of the largest antichain (a set of elements that are incomparable). In simpler terms, it helps us understand how to organize items in a hierarchy while highlighting the balance between the largest independent group and the arrangement of those items in ordered sequences.