Applying the TemperleyLieb Algebra to the 4Colour TheoremSabin CautisHarvard University
April 7,

ABSTRACT


The TemperleyLieb algebra $TL_n(q)$ is a deformation of the symmetric group algebra coming from statistical mechanics. Some of its neat properties may be seen by relating it to the meander problem (counting nonintersecting closed planar paths through $2n$ fixed points on the line). We will motivate a generalization $TL_n(x,y)$ of $TL_n(q)$ via an attempt to understand the BirkhoffLewis equations (which some hope may be used to give an algebraic proof of the fourcolour theorem). $TL_n(x,y)$ is related to generalized Chebyshev polynomials and in a way is the greatest generalization we can make without losing many of the nice properties of $TL_n(q)$. This talk is accessible to a general audience and presents joint work with David Jackson. 
Combinatorics Seminar, Mathematics Department, MIT, sara(atsign)math.mit.edu 

