The writhe of permutations and random framed knots1. Issue 1 (17th November 2016)

• Record Type: Journal Article
• Authors: Even‐Zohar, Chaim
• Is Part Of: Random structures & algorithms. Volume 51:Issue 1(2017)
• Page Start: 121
• Page End: 142
• Publication Date: 2016-11-17
• Subjects: writhe -- permutation statistics -- framed knot -- random knot -- circular rank correlation -- method of moments; Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20704
• Languages: English
• ISSNs: 1042-9832

Abstract

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, studied with Hass, Linial, and Nowik (Discrete Comput Geom, 2016). The distribution of the framing in this model is equivalent to the writhe of random permutations. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 121–142, 2017