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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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Folding and coloring problems in mathematics and physics
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by P. Di Francesco PDF
Bull. Amer. Math. Soc. 37 (2000), 251-307 Request permission


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:
  • 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.
  • © Copyright 2000 American Mathematical Society
  • 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:
  • MathSciNet review: 1754642