A Diagrammatic Approach to the Meander Problem

Details A Diagrammatic Approach to the Meander Problem A Diagrammatic Approach to the Meander Problem

1998-07-27

arxiv.org/abs/hep-th/9807193v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX 25 pages, 22 figures

Scientific paper

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.

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