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Multivariate Eulerian Polynomials and Exclusion Processes

Published online by Cambridge University Press:  18 March 2016

P. BRÄNDÉN
Affiliation:
Department of Mathematics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden (e-mail: pbranden@kth.se, visontai@kth.se)
M. LEANDER
Affiliation:
Department of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden (e-mail: madde@math.su.se)
M. VISONTAI
Affiliation:
Department of Mathematics, Royal Institute of Technology, SE-100 44, Stockholm, Sweden (e-mail: pbranden@kth.se, visontai@kth.se)

Abstract

We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and coloured permutations. The corresponding expressions of the multivariate partition functions are then related to multivariate generalisations of Eulerian polynomials for coloured permutations considered recently by N. Williams and the third author, and others. We also discuss stability and negative dependence properties satisfied by the partition functions.

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Paper
Copyright
Copyright © Cambridge University Press 2016 

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