Recurrence relations in counting the pattern 13-2 in flattened permutations

TL;DR

This paper demonstrates that the generating function counting flattened permutations with a specific pattern occurrence is rational, utilizing recurrence relations and the kernel method.

Contribution

It introduces a novel approach to prove the rationality of the generating function for pattern 13-2 in flattened permutations using recurrence relations and the kernel method.

Findings

The generating function for pattern 13-2 occurrences is rational.

Recurrence relations are effectively used to analyze pattern counts.

The kernel method facilitates the proof of rationality.

Abstract

We prove that the generating function for the number of flattened permutations having a given number of occurrences of the pattern 13-2 is rational, by using the recurrence relations and the kernel method.