  The meander problem is a combinatorial problem which provides a toy model of
the compact folding of polymer chains. In this paper we study various questions
relating to the enumeration of meander diagrams, using diagrammatical methods.
By studying the problem of folding tree graphs, we derive a lower bound on the
exponential behaviour of the number of connected meander diagrams. A different
diagrammatical method, based on a non-commutative algebra, provides an
approximate calculation of the behaviour of the generating functions for both
meander and semi-meander diagrams.
