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arXiv · 1712.05776

The HOMFLY-PT polynomial is fixed-parameter tractable

Benjamin A. Burton
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Abstract

Many polynomial invariants of knots and links, including the Jones and HOMFLY-PT polynomials, are widely used in practice but #P-hard to compute. It was shown by Makowsky in 2001 that computing the Jones polynomial is fixed-parameter tractable in the treewidth of the link diagram, but the parameterised complexity of the more powerful HOMFLY-PT polynomial remained an open problem. Here we show that computing HOMFLY-PT is fixed-parameter tractable in the treewidth, and we give the first sub-exponential time algorithm to compute it for arbitrary links.

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Benjamin A. Burton. 2017-12-15. The HOMFLY-PT polynomial is fixed-parameter tractable. https://arxiv.org/abs/1712.05776

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