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arXiv · 1511.09469

The Writhe of Permutations and Random Framed Knots

Chaim Even-Zohar
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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.

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Chaim Even-Zohar. 2016-12-29. The Writhe of Permutations and Random Framed Knots. https://doi.org/10.1002/rsa.20704

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