Experimental Mathematics

A Markov Chain on the Symmetric Group That Is Schubert Positive?

Thomas Lam and Lauren Williams

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Abstract

We study a multivariate Markov chain on the symmetric group with remarkable enumerative properties. We conjecture that the stationary distribution of this Markov chain can be expressed in terms of positive sums of Schubert polynomials. This Markov chain is a multivariate generalization of a Markov chain introduced by the first author in the study of random affine Weyl group elements.

Article information

Source
Experiment. Math., Volume 21, Issue 2 (2012), 189-192.

Dates
First available in Project Euclid: 31 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.em/1338430829

Mathematical Reviews number (MathSciNet)
MR2931313

Zentralblatt MATH identifier
1243.05240

Subjects
Primary: 05E05: Symmetric functions and generalizations 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Markov chain Schubert polynomials symmetric group

Citation

Lam, Thomas; Williams, Lauren. A Markov Chain on the Symmetric Group That Is Schubert Positive?. Experiment. Math. 21 (2012), no. 2, 189--192. https://projecteuclid.org/euclid.em/1338430829


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