Chains and Antichains
Partial ordered sets provide a common frame for many combinatorial configurations. Formally, a partially ordered set (or poset, for short) is a set P together with a binary relation < between its elements which is transitive and irreflexive: if x < y and y < z then x < z, but x < y and y < x cannot both hold. We write x ⩽ y if x < y or x = y. Elements x and y are comparable if either x ⩽ y or y ⩽ x (or both) hold.
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