Enumeration of planar Tangles
Combinatorics
2021-03-09 v3
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.
Keywords
Cite
@article{arxiv.1906.01541,
title = {Enumeration of planar Tangles},
author = {Douglas A. Torrance},
journal= {arXiv preprint arXiv:1906.01541},
year = {2021}
}
Comments
improved figures, simplified proof of area, and new rows in Table 4.1 for the m = 10 case