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 [m1, ⋯, mr] when log(r+1) ≤ min{mi}. It is also shown how to derive good estimates for the packing density of permutations of type [k, 1, k] when k ≥ 3. Both results are based on establishing the number of layers in near optimal permutations using a layer-merging technique.
CITATION STYLE
Hästö, P. A. (2002). The packing density of other layered permutations. Electronic Journal of Combinatorics, 9(2 R). https://doi.org/10.37236/1673
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