Geodesic
Random cyclations
Nicholas Pippenger1
1Harvey Mudd College
The electronic journal of combinatorics, Tome 20 (2013) no. 4
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Consider $n$ unit intervals, say $[1,2], [3,4], \ldots, [2n-1,2n]$. Identify their endpoints in pairs at random, with all $(2n-1)!! = (2n-1)(2n-3)\cdots 3\cdot 1$ 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.
DOI : 10.37236/3643
Classification : 05A05, 60C05
Mots-clés : permutations, cycle lengths, asymptotics

Nicholas Pippenger  1

1 Harvey Mudd College 
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Nicholas Pippenger. Random cyclations. The electronic journal of combinatorics, Tome 20 (2013) no. 4. doi: 10.37236/3643

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