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Gauss diagram formulae for Vassiliev invariants from Kauffman polynomial

Published 2 Jun 2023 in math.GT and math.CO | (2306.01591v1)

Abstract: A state model for Kauffman polynomial of Dubrovnik-version is given. Based on the state model, the Gauss diagram formulae for Vassiliev invariants are given from the coefficients of Kauffman polynomial following the method of Chmutov and Polyak. Some arrow diagram identities are given to simplify the Gauss diagram formulae of order 3, which give Polyak-Viro and Chmutov-Polyak formulae for the Vassiliev invariant of order 3. The models of Kauffman polynomial and HOMFLY-PT polynomial give different Gauss diagram expressions when specializing to Jones poynomial.

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