Enumeration of meander configurations

Determine the general enumeration of meander configurations and their precise asymptotic behavior as the number of intersection points tends to infinity.

Background

The paper studies singular meanders, in which tangencies are allowed, and contrasts them with the classical non-singular meander problem. Although substantial progress has been made on meander enumeration, the authors identify the general counting problem and the precise asymptotic behavior of meander numbers as unresolved. This problem concerns the classical meander numbers, rather than the s-meandric permutation counts that are analyzed further in the paper.