On irreducible meanders growth rate

TL;DR

This paper investigates the growth rate of irreducible meanders, establishing bounds that show their proportion among prime meanders diminishes to zero as the order increases.

Contribution

It provides new upper and lower bounds for the growth rate of irreducible meanders and analyzes their asymptotic behavior among prime meanders.

Findings

Upper bound for irreducible meanders growth rate

Lower bound for irreducible meanders growth rate

Proportion of irreducible meanders approaches zero as n increases

Abstract

In this article, we provide upper and lower bounds for the growth rate of irreducible meanders. The obtained upper bound implies that the proportion of irreducible meanders among all of the prime meanders of order $n$ approaches $0$ as $n$ approaches infinity.