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Fragmenting random permutations

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Goldschmidt, C. (Christina), Martin, James B. and Spanò, Dario. (2008) Fragmenting random permutations. Electronic communications in probability, Vol.13 (No.44). pp. 461-474. ISSN 1083-589X

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Abstract

Problem 1.5.7 from Pitman's Saint-Flour lecture notes [11]: Does there exist for each n a fragmentation process (Pi(n,k); 1 <= k <= n) such that Pi(n,k) is distributed like the partition generated by cycles of a uniform random permutation of {1, 2,...,n} conditioned to have k cycles? We show that the answer is yes. We also give a partial extension to general exchangeable Gibbs partitions.

Item Type:

Journal Article

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Permutations

Journal or Publication Title:

Electronic communications in probability

Publisher:

University of Washington. Dept. of Mathematics

ISSN:

1083-589X

Official Date:

14 August 2008

Dates:

Date	Event
14 August 2008	Published

Volume:

Vol.13

Number:

No.44

Number of Pages:

Page Range:

pp. 461-474

Status:

Peer Reviewed

Publication Status:

Published

Access rights to Published version:

Open Access

Funder:

Engineering and Physical Sciences Research Council (EPSRC)

Grant number:

EP/D065755/1 (EPSRC), GR/T21783/01 (EPSRC)

References:

[1] N. Berestycki and J. Pitman. Gibbs distributions for random partitions generated by a
fragmentation process. J. Stat. Phys., 127(2):381–418, 2007.
[2] B. Efron. Increasing properties of P´olya frequency functions. Ann. Math. Statist., 36:272–
279, 1965.
[3] P. Elias, A. Feinstein, and C. Shannon. A note on the maximum flow through a network.
Institute of Radio Engineers, Transactions on Information Theory, IT-2:117–119, 1956.
[4] L. R. Ford, Jr. and D. R. Fulkerson. Maximal flow through a network. Canad. J. Math.,
8:399–404, 1956.
[5] A. Gnedin and J. Pitman. Exchangeable Gibbs partitions and Stirling triangles. J. Math.
Sci. (N. Y.), 138(3):5677–5685, 2006. Translated from Zapiski Nauchnykh Seminarov
POMI, Vol. 325, 2005, pp. 83–102.
[6] P. Hall. On representatives of subsets. J. London Math. Soc., 10:26–30, 1935.
[7] S. G. Hoggar. Chromatic polynomials and logarithmic concavity. J. Combinatorial Theory
Ser. B, 16, 1974.
[8] T. Kamae, U. Krengel, and G. L. O’Brien. Stochastic inequalities on partially ordered
spaces. Ann. Probab., 5(6):899–912, 1977.
[9] J. Pitman. Combinatorial stochastic processes, volume 1875 of Lecture Notes in Mathematics.
Springer-Verlag, Berlin, 2006. Lectures from the 32nd Summer School on Probability
Theory held in Saint-Flour, July 7–24, 2002.
[10] J. Pitman and M. Yor. The two-parameter Poisson-Dirichlet distribution derived from a
stable subordinator. Ann. Probab., 25(2):855–900, 1997.
[11] B. E. Sagan. Inductive and injective proofs of log concavity results. Discrete Math., 68(2-
3):281–292, 1988.