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Separation Probabilities for Products of Permutations

Published online by Cambridge University Press:  13 December 2013

OLIVIER BERNARDI ,
ROSENA R. X. DU ,
ALEJANDRO H. MORALES  and
RICHARD P. STANLEY
OLIVIER BERNARDI
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology; Cambridge, MAUSA02139 (e-mail: bernardi@math.mit.edu, ahmorales@math.mit.edu, rstan@math.mit.edu)
ROSENA R. X. DU
Affiliation:
Department of Mathematics, East China Normal University; Shanghai, China200041 (e-mail: rxdu@math.ecnu.edu.cn)
ALEJANDRO H. MORALES
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology; Cambridge, MAUSA02139 (e-mail: bernardi@math.mit.edu, ahmorales@math.mit.edu, rstan@math.mit.edu)
RICHARD P. STANLEY
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology; Cambridge, MAUSA02139 (e-mail: bernardi@math.mit.edu, ahmorales@math.mit.edu, rstan@math.mit.edu)
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Abstract

We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements 1,2,. . .,k are in distinct cycles of the random permutation of {1,2,. . .,n} obtained as a product of two uniformly random n-cycles.

Keywords

Primary 05A05Secondary 05E0560C05

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 2 , March 2014 , pp. 201 - 222
Copyright
Copyright © Cambridge University Press 2013 

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