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{\bf Cathleen Battiste Presutti}
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{\bf Determining Lower Bounds for Packing Densities of Non-layered Patterns Using Weighted Templates}
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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.



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