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Corpus ID: 119671541

Sigma-Adequate Link Diagrams and the Tutte Polynomial

@article{Giambrone2016SigmaAdequateLD,
title={Sigma-Adequate Link Diagrams and the Tutte Polynomial},
author={A. Giambrone},
journal={arXiv: Geometric Topology},
year={2016}
}

In this paper, we characterize the sigma-adequacy of a link diagram in two ways: in terms of a certain edge subset of its Tait graph and in terms of a certain product of Tutte polynomials. Furthermore, we show that the symmetrized Tutte polynomial of the Tait graph of a link diagram can be written as a sum of these products of Tutte polynomials, where the sum is over the sigma-adequate states of the given link diagram. Using this state sum, we show that the number of sigma-adequate states of a… Expand