Enumeration of planar Tangles
arXiv:1906.01541 · doi:10.1007/s12044-020-00575-7
Abstract
A planar Tangle is a smooth simple closed curve piecewise defined by quadrants of circles with constant curvature. We can enumerate Tangles by counting their dual graphs, which consist of a certain family of polysticks. The number of Tangles with a given length or area grows exponentially, and we show the existence of their growth constants by comparing Tangles to two families of polyominoes.
improved figures, simplified proof of area, and new rows in Table 4.1 for the m = 10 case