Jakub Sliacan ; Walter Stromquist - Improving bounds on packing densities of 4-point permutations

dmtcs:3286 - Discrete Mathematics & Theoretical Computer Science, February 6, 2018, Vol. 19 no. 2, Permutation Patterns 2016 - https://doi.org/10.23638/DMTCS-19-2-3
Improving bounds on packing densities of 4-point permutations

Authors: Jakub Sliacan ; Walter Stromquist

    We consolidate what is currently known about packing densities of 4-point permutations and in the process improve the lower bounds for the packing densities of 1324 and 1342. We also provide rigorous upper bounds for the packing densities of 1324, 1342, and 2413. All our bounds are within $10^{-4}$ of the true packing densities. Together with the known bounds, this gives us a fairly complete picture of all 4-point packing densities. We also provide new upper bounds for several small permutations of length at least five. Our main tool for the upper bounds is the framework of flag algebras introduced by Razborov in 2007.


    Volume: Vol. 19 no. 2, Permutation Patterns 2016
    Section: Permutation Patterns
    Published on: February 6, 2018
    Accepted on: February 6, 2018
    Submitted on: April 26, 2017
    Keywords: Mathematics - Combinatorics

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