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{\bf Peter A. H\"ast\"o}
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{\bf The Packing Density of Other Layered Permutations}
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In this paper the packing density of various layered permutations is
calculated, thus solving some problems suggested by Albert, Atkinson,
Handley, Holton $\&$ Stromquist [Electron. J. Combin.{~\bf 9}
(2002), $\#$R5]. Specifically, the density is found for layered
permutations of type $[m_1, \ldots, m_r]$ when $\log(r+1)\le \min\{
m_i\}$. It is also shown how to derive good estimates for the packing
density of permutations of type $[k,1,k]$ when $k\ge 3$. Both results
are based on establishing the number of layers in near optimal
permutations using a layer-merging technique.
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