The 2-colored operad on the set of singular meanders

TL;DR

This paper extends a geometric decomposition of meanders to singular meanders, providing a more algebraic framework for understanding their structure and properties.

Contribution

It generalizes previous work on meanders by introducing a new algebraic approach to singular meanders, broadening the theoretical understanding.

Findings

Developed a geometric decomposition for singular meanders

Provided an algebraic description of the decomposition

Enhanced the theoretical framework for studying meanders

Abstract

In the recent work arXiv:2112.10289 we introduced a geometric decomposition of meanders. In the present paper, we generalize this approach to the case of singular meanders and give a more algebraic description of this decomposition.