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

DOI:
https://doi.org/10.1090/S0002-9939-2012-11283-3

Published electronically:
April 19, 2012

MathSciNet review:
2957227

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Abstract | References | Similar Articles | Additional Information

Abstract: We present a simple formula for the expected number of inversions in a permutation of size obtained by applying 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 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:
https://doi.org/10.1090/S0002-9939-2012-11283-3

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.