Random cyclations
Combinatorics
2007-05-23 v1
Abstract
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and we investigate the distribution of these lengths. The distribution is similar to that of the distribution of the lengths of cycles in a random permutation, but it also exhibits some striking differences.
Cite
@article{arxiv.math/0408031,
title = {Random cyclations},
author = {Nicholas Pippenger},
journal= {arXiv preprint arXiv:math/0408031},
year = {2007}
}
Comments
i+19 pp