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The packing density of other layered permutations
The electronic journal of combinatorics, Permutation Patterns, Tome 9 (2002) no. 2
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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. 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.
DOI : 10.37236/1673
Classification : 05A05, 05A16 
@article{10_37236_1673,
     author = {Peter A. H\"ast\"o},
     title = {The packing density of other layered permutations},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     number = {2},
     doi = {10.37236/1673},
     zbl = {1037.05001},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1673/}
}
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Peter A. Hästö. The packing density of other layered permutations. The electronic journal of combinatorics, Permutation Patterns, Tome 9 (2002) no. 2. doi: 10.37236/1673

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