Tutte Chromatic Identities from the Temperley-lieb Algebra

Abstract

One remarkable feature of the chromatic polynomial χ(Q) is Tutte’s golden identity. This relates χ(φ+ 2) for any triangulation of the sphere to (χ(φ+ 1)) for the same graph, where φ denotes the golden ratio. We explain how this result fits in the framework of quantum topology and give a proof using the chromatic algebra, whose Markov trace is the chromatic… (More)

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