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An algebraic approach to the planar coloring problem

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Abstract

We point out a general relationship between the planar coloring problem withQ colors and the Temperley-Lieb algebra with parameter\(\sqrt Q \). This allows us to give a complete algebraic reformulation of the four color result, and to give algebraic interpretations of various other aspects of planar colorings.

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Communicated by N. Yu. Reshetikhin

Work supported in part by NSF Grant #DMS-882602, the program for Mathematics and Molecular Biology, UC Berkeley, and a visiting fellowship of the Japan Society for the promotion of science at Kyoto University, Kyoto, Japan

Work supported in part by DOE Contact #DE-AC02-76ERO3075 and by a Packard Fellowship for Science and Engineering

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Kauffmann, Saleur, H. An algebraic approach to the planar coloring problem. Commun.Math. Phys. 152, 565–590 (1993). https://doi.org/10.1007/BF02096619

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