The Writhe of Permutations and Random Framed Knots
Combinatorics
2017-11-30 v3 Geometric Topology
Abstract
We introduce and study the writhe of a permutation, a circular variant of the well-known inversion number. This simple permutation statistics has several interpretations, which lead to some interesting properties. For a permutation sampled uniformly at random, we study the asymptotics of the writhe, and obtain a non-Gaussian limit distribution. This work is motivated by the study of random knots. A model for random framed knots is described, which refines the Petaluma model. The distribution of the framing in this model is equivalent to the writhe of random permutations.
Cite
@article{arxiv.1511.09469,
title = {The Writhe of Permutations and Random Framed Knots},
author = {Chaim Even-Zohar},
journal= {arXiv preprint arXiv:1511.09469},
year = {2017}
}