Inversion Monotonicity in Subclasses of the 1324-avoiders
Submitted to Combinatorial Theory
Anders, Svante, Henning and Emil
We prove that the pattern collections ${1324, 231}$ and ${1324, 2314, 3214, 4213}$ are inversion monotone via explicit injections, making progress on a conjecture from 2012. We characterize which pattern sets have limit sequences and determine these sequences for all pairs of patterns of length four involving 1324. Extending earlier work on decomposable permutations, we identify a broader family of inversion-monotone sets and obtain an enumeration formula for certain restricted permutations.