Electronic Journal of Probability

Asymptotic independence in large random permutations with fixed descent set

Pierre Tarrago

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Ehrenborg, Levin and Readdy have introduced a new probabilistic approachto the combinatorics of permutations with fixed set of descents. In this paper we extend this approach by introducing a more general probabilistic model. The study ofthis model yields new estimates on the behavior of a uniform random permutation σhaving a fixed descent set. In particular, we find a positive answer to a conjecture and we show that independently of the shape of the descent set, $σ(i)$ and $σ(j)$ are almost independent when $i − j$ becomes large.

Article information

Electron. J. Probab., Volume 20 (2015), paper no. 103, 33 pp.

Accepted: 6 October 2015
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05A16: Asymptotic enumeration
Secondary: 60C05: Combinatorial probability 60F05: Central limit and other weak theorems

Compositions descent set permutation asymptotic independence

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Tarrago, Pierre. Asymptotic independence in large random permutations with fixed descent set. Electron. J. Probab. 20 (2015), paper no. 103, 33 pp. doi:10.1214/EJP.v20-4196. https://projecteuclid.org/euclid.ejp/1465067209

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