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This paper gives a detailed overview of the Tutte polynomial and proves results that are simply stated in most of the current literature. It covers basic graph theory and matroid theory, basic properties of the Tutte polynomial, the recipe theorem and two applications of the recipe theorem: one to the Potts model and Ising model of statistical physics and one to the HOMFLY polynomial in knot theory.
Graph theory -- Tutte polynomial -- Recipe theorem, Matroids -- Theory, Statistical mechanics -- Potts Model, Ising model, Knot Theory -- Knot Polynomials, Knot Theory -- Homfly Polynomials, Whitman College -- Dissertation collection 2015 -- Mathematics Department
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