Prime Factorization of Meanders

TL;DR

This paper introduces a prime factorization framework for open meanders using 2-colored operads, enabling efficient enumeration and analysis of their asymptotic behavior.

Contribution

It presents a novel prime factorization approach for open meanders, linking their enumeration to irreducible meanders and providing asymptotic results.

Findings

Efficient enumeration of iterated snakes

Reduction of meander enumeration to irreducible meanders

Asymptotic behavior analysis of meanders

Abstract

In this paper, we introduce a prime factorization of open meanders, articulated through the framework of 2-colored operads. We demonstrate that each open meander can be canonically constructed from building blocks of two types: iterated snakes and irreducible meanders. We find out that iterated snakes allow efficient enumeration, and thus the problem of enumerating meanders reduces to the problem of enumerating irreducible meanders. Additionally, we present some results concerning the asymptotic of meanders of both classes.