Plane Meanders

Meanders form a set of combinatorial problems concerned with the enumeration of self-avoiding curves crossing a line through a given number of points. Meanders are considered distinct up to any smooth deformation. This problem seems to date back at least to work of Poincare on differential geometry. Since then it has from time to time been studied by mathematicians in various contexts such as the folding of a strip of stamps or folding of maps. During the last decade or so has it has received considerable attention in other areas of science. In computer science meanders are related to the sorting of Jordan sequences and have been used for lower bound arguments. In physics meanders are relevant to the study of compact foldings of polymers.