Electronic Journal of Probability

Asymptotic independence in large random permutations with fixed descent set

Pierre Tarrago

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465067209

Digital Object Identifier
doi:10.1214/EJP.v20-4196

Mathematical Reviews number (MathSciNet)
MR3407220

Zentralblatt MATH identifier
1326.05013

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

Keywords
Compositions descent set permutation asymptotic independence

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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