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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Expected length of a product of random reflections


Author: Jonas Sjöstrand
Journal: Proc. Amer. Math. Soc. 140 (2012), 4369-4380
MSC (2010): Primary 60J10; Secondary 05A05
Published electronically: April 19, 2012
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Abstract: We present a simple formula for the expected number of inversions in a permutation of size $ n$ obtained by applying $ t$ random (not necessarily adjacent) transpositions to the identity permutation. More generally, for any finite irreducible Coxeter group belonging to one of the infinite families (type A, B, D, and I), an exact expression is obtained for the expected length of a product of $ t$ random reflections.


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Additional Information

Jonas Sjöstrand
Affiliation: Department of Mathematics, Royal Institute of Technology SE-100 44 Stockholm, Sweden
Email: jonass@kth.se

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11283-3
PII: S 0002-9939(2012)11283-3
Keywords: Permutation, transposition, inversion, Coxeter group, reflection, absolute length
Received by editor(s): November 24, 2010
Received by editor(s) in revised form: May 31, 2011
Published electronically: April 19, 2012
Communicated by: Jim Haglund
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.