A state enumeration of the foil knot
Published in arXiv e-Print archive, 2017
We split the crossings of the foil knot and enumerate the resulting states with a generating polynomial. Unexpectedly, the number of such states which consist of two components are given by the lazy caterer’s sequence. This sequence describes the maximum number of planar regions that is obtained with a given number of straight lines. We then establish a bijection between this partition of the plane and the concerned foil splits sequence.
Recommended citation: Franck Ramaharo and Fanja Rakotondrajao (2017), "A state enumeration of the foil knot", arXiv e-Print archive, arXiv:1712.04026 [math.CO].
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