Call a permutation $k$-inflatable if the sequence of its tensor products with uniform random permutations of increasing lengths has uniform $k$-point pattern densities. Previous work has shown that nontrivial $k$-inflatable permutations do not exist for $k \geq 4$. In this paper, we derive a general formula for the limit densities of patterns in the sequence of tensor products of a fixed permutation with each permutation from a convergent sequence. By applying this result, we completely characterize $3$-inflatable permutations and find explicit examples of $3$-inflatable permutations with various lengths, including the shortest examples with length $17$.
@article{10_37236_8234,
author = {Tanya Khovanova and Eric Zhang},
title = {Limit densities of patterns in permutation inflations},
journal = {The electronic journal of combinatorics},
year = {2021},
volume = {28},
number = {1},
doi = {10.37236/8234},
zbl = {1456.05003},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8234/}
}
TY - JOUR
AU - Tanya Khovanova
AU - Eric Zhang
TI - Limit densities of patterns in permutation inflations
JO - The electronic journal of combinatorics
PY - 2021
VL - 28
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8234/
DO - 10.37236/8234
ID - 10_37236_8234
ER -
%0 Journal Article
%A Tanya Khovanova
%A Eric Zhang
%T Limit densities of patterns in permutation inflations
%J The electronic journal of combinatorics
%D 2021
%V 28
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8234/
%R 10.37236/8234
%F 10_37236_8234
Tanya Khovanova; Eric Zhang. Limit densities of patterns in permutation inflations. The electronic journal of combinatorics, Tome 28 (2021) no. 1. doi: 10.37236/8234
