Nonrationality and Principal permutation classes: the remaining case

TL;DR

This paper proves that all principal permutation classes generated by patterns longer than two have nonrational generating functions, completing the classification of their generating function types.

Contribution

It completes the proof that principal permutation classes with patterns longer than two have nonrational generating functions, filling a key gap in permutation class theory.

Findings

All principal permutation classes generated by patterns longer than two have nonrational generating functions.

The proof completes the classification of generating functions for these classes.

This result advances understanding of the algebraic nature of permutation class generating functions.

Abstract

We complete the proof of the fact that all principal permutation classes generated by a pattern longer than two have a nonrational generating function.