Algorithmic enumeration of genus-one knot and link diagrams up to 8 crossings via cellular 4-regular torus maps encoded by permutation pairs, producing over 33,000 types plus structural facts.
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Reshetikhin-Turaev knot polynomials are fixed-parameter tractable in the treewidth of the input diagram via tensor network contraction, yielding e^{O(sqrt n)} time.
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Exhaustive Generation of Genus-One Knot and Link Diagrams via Maps on the Torus
Algorithmic enumeration of genus-one knot and link diagrams up to 8 crossings via cellular 4-regular torus maps encoded by permutation pairs, producing over 33,000 types plus structural facts.
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Fixed-parameter tractable computation of Reshetikhin--Turaev knot polynomials via tensor networks
Reshetikhin-Turaev knot polynomials are fixed-parameter tractable in the treewidth of the input diagram via tensor network contraction, yielding e^{O(sqrt n)} time.