Expected length of a product of random reflections
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- by Jonas Sjöstrand PDF
- Proc. Amer. Math. Soc. 140 (2012), 4369-4380 Request permission
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.References
- Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005. MR 2133266
- Mireille Bousquet-Mélou, The expected number of inversions after $n$ adjacent transpositions, Discrete Math. Theor. Comput. Sci. 12 (2010), no. 2, 65–88. MR 2676666
- Niklas Eriksen, Expected number of inversions after a sequence of random adjacent transpositions—an exact expression, Discrete Math. 298 (2005), no. 1-3, 155–168. MR 2163446, DOI 10.1016/j.disc.2004.09.015
- Niklas Eriksen and Axel Hultman, Estimating the expected reversal distance after a fixed number of reversals, Adv. in Appl. Math. 32 (2004), no. 3, 439–453. MR 2041958, DOI 10.1016/S0196-8858(03)00054-X
- Niklas Eriksen and Axel Hultman, Expected reflection distance in $G(r,1,n)$ after a fixed number of reflections, Ann. Comb. 9 (2005), no. 1, 21–33. MR 2135773, DOI 10.1007/s00026-005-0238-y
- Henrik Eriksson, Kimmo Eriksson, and Jonas Sjöstrand, Expected number of inversions after a sequence of random adjacent transpositions, Formal power series and algebraic combinatorics (Moscow, 2000) Springer, Berlin, 2000, pp. 677–685. MR 1798262
- Andreas Jönsson, Evolutionary fixed point distance problems, master’s thesis, University of Gothenburg, 2009.
- Emma Troili, Förväntade avstånd i Coxetergrupper [Expected distances in Coxeter groups], master’s thesis, KTH, 2002, in Swedish.
Additional Information
- Jonas Sjöstrand
- Affiliation: Department of Mathematics, Royal Institute of Technology , SE-100 44 Stockholm, Sweden
- Email: jonass@kth.se
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2957227