Random cyclations

Details Random cyclations Random cyclations

2004-08-03

arxiv.org/abs/math/0408031v1

Mathematics

Combinatorics

i+19 pp

Scientific paper

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.

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