Determining lower bounds for packing densities of non-layered patterns using weighted templates (Q1010765)

Summary: The packing density of a permutation pattern \(\pi\) is the limiting value, \({n}\rightarrow\infty\), of the maximum proportion of subsequences of \(\sigma\in{S_{n}}\) that are order-isomorphic to \(\pi\). We generalize methods for obtaining lower bounds for the packing density of any pattern and demonstrate the methods' usefulness when patterns are non-layered.