Growth Rates for Subclasses of $\mathrm{Av}(321)$

Abstract

Pattern classes which avoid $321$ and other patterns are shown to have the same growth rates as similar (but strictly larger) classes obtained by adding articulation points to any or all of the other patterns. The method of proof is to show that the elements of the latter classes can be represented as bounded merges of elements of the original class, and that the bounded merge construction does not change growth rates.