Pattern Avoidance in Poset Permutations

Sam Hopkins, Morgan Weiler

Published 2012-08-28, updated 2015-01-02Version 4

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 a is denoted Av_P(a). We extend a proof of Simion and Schmidt to show that Av_P (132) <= Av_P (123) for any poset P, and we exactly classify the posets for which equality holds.