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A Generating Series for Murakami-Ohtsuki-Yamada Graph Evaluations
Stavros Garoufalidis
,
Roland van der Veen
Abstract
Murakami-Ohtsuki-Yamada introduced an evaluation of certain oriented planar trivalent graphs with colored edges. This evaluation plays a key role in the evaluation of the colored HOMFLY polynomial of a link in 3-space and its Khovanov-Rozansky categorification. Our goal is to give a generating series formula for the evaluation of MOY graphs, which may be useful in categorification, and in the study of $q$-holonomicity of the colored HOMFLY polynomial.