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math.GT2024
FlatKnotInfo: the first 1.24 million flat knots
Jie Chen
We use matchings on Lyndon words to classify flat knots up to 8 crossings. Using flat knots invariants such as the based matrix, the -invariant, the flat arrow polynomial, and…
math.GT2024
Connected sum and crossing numbers of flat virtual knots
Jie Chen
The connected sum of two flat virtual knots depends on the choice of diagrams and basepoints. We show that any minimal crossing diagram of a composite flat virtual knot is a connec…