Pattern Avoidance in Poset Permutations.

We extend the concept of pattern avoidance in permutations on a totally ordered set to pattern avoidance in permutations on partially ordered sets. The number of permutations on P that avoid the pattern π is denoted AvP (π). We extend a proof of Simion and Schmidt to show that AvP (132) ≤ AvP (123) for any poset P, and we exactly classify the posets for which equality holds. [ABSTRACT FROM AUTHOR]