On 3-Inflatable Permutations
Tanya Khovanova, Eric Zhang · arXiv (Cornell University) · 2018
Call a permutation $k$-inflatable if it can be blown up into a convergent sequence of permutations by a uniform inflation construction, such that this sequence is symmetric with respect to densities of induced subpermutations of length $k$. We study properties of 3-inflatable permutations, finding a general formula for limit densities of pattern permutations in the uniform inflation of a given permutation. We also characterize and find examples of $3$-inflatable permutations of various lengths, including the shortest examples with length $17$.