Permutation Patterns: St. Andrews 2007
We give a new lower bound of 0.10472422757673209041 for the packing density of 2413, justify it by a construction, and conjecture that this value is actually equal to the packing density. Along the way we define the packing rate of a permutation with respect to a measure, and show that maximizing the packing rate of a pattern over all measures gives the packing density of the pattern.
Cambridge University Press
S. Linton, N. Ruškuc, V. Vatter
C. B. Presutti and Walter Stromquist.
"Packing Rates Of Measures And A Conjecture For The Packing Density Of 2413".
Permutation Patterns: St. Andrews 2007.