A New Way to Tabulate Knots

Lisa Hernandez; Xiao-Song Lin

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A New Way to Tabulate Knots

Lisa Hernandez·Xiao-Song Lin

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Abstract

We introduce a new way to tabulate knots by representing knot diagrams using a pair of planar trees. This pair of trees have their edges labeled by integers, they have no valence 2 vertices, and they have the same number of valence 1 vertices. The number of valence 1 vertices of the trees is called the girth of the knot diagram. The classification problem of knots admitting girth 2 and 3 diagrams is studied. The planar tree pair representations of girth less than 4 for knot diagrams in Rolfsen's table are given.

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Lisa Hernandez, Xiao-Song Lin. 2005-08-29. A New Way to Tabulate Knots. https://arxiv.org/abs/math/0508590

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