Pin Classes I: Growth Rates

TL;DR

This paper investigates permutation classes derived from infinite pin sequences, demonstrating they have proper growth rates and providing a method to compute these rates.

Contribution

It introduces a new approach to determine growth rates of permutation classes from infinite pin sequences, a previously unexplored area.

Findings

Permutation classes from infinite pin sequences have proper growth rates.

A procedure for calculating these growth rates is established.

The study advances understanding of the structural complexity of permutation classes.

Abstract

Pin sequences play an important role in the structural study of permutation classes. In this paper, we study the permutation classes that comprise all the finite subpermutations contained in an infinite pin sequence. We prove that these permutation classes have proper growth rates and establish a procedure for calculating these growth rates.