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2015 Asymptotic independence in large random permutations with fixed descent set
Pierre Tarrago
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Electron. J. Probab. 20: 1-33 (2015). DOI: 10.1214/EJP.v20-4196

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.

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Pierre Tarrago. "Asymptotic independence in large random permutations with fixed descent set." Electron. J. Probab. 20 1 - 33, 2015. https://doi.org/10.1214/EJP.v20-4196

Information

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

zbMATH: 1326.05013
MathSciNet: MR3407220
Digital Object Identifier: 10.1214/EJP.v20-4196

Subjects:
Primary: 05A16
Secondary: 60C05 , 60F05

Keywords: Asymptotic independence , compositions , descent set , permutation

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