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Folding and coloring problems in mathematics and physics


Author: P. Di Francesco
Journal: Bull. Amer. Math. Soc. 37 (2000), 251-307
MSC (2000): Primary 82-02; Secondary 82B20, 82B41, 83C27, 05A15, 05A16, 05C15, 05C30, 05C80, 05E99, 03D20, 16G99
DOI: https://doi.org/10.1090/S0273-0979-00-00870-3
Published electronically: April 10, 2000
MathSciNet review: 1754642
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Abstract: We review various folding problems arising in the physics of membranes and polymers. These are (1) the phantom folding of tethered membranes, i.e. the two-dimensional lattice folding; (2) the phantom folding of fluid membranes, i.e. the folding of tessellations of arbitrary genus; (3) the self-avoiding folding of polymers, i.e. the meander problem. All three problems are found to be related to coloring problems and possess one kind of underlying integrable structure, in different guises. Many mathematical results follow from taking advantage of this fact.


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Additional Information

P. Di Francesco
Affiliation: Service de Physique Théorique, C.E.A. Saclay, F-91191 Gif sur Yvette, France
Email: philippe@spht.saclay.cea.fr

Received by editor(s): November 19, 1998
Received by editor(s) in revised form: February 10, 2000
Published electronically: April 10, 2000
Additional Notes: Work partially supported by NSF grant PHY-9722060.
Article copyright: © Copyright 2000 American Mathematical Society