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Permutation statistics of products of random permutations
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: Advances in Applied Mathematics, ISSN 0196-8858, E-ISSN 1090-2074, Vol. 54, 1-10 p.Article in journal (Refereed) Published
Abstract [en]

Given a permutation statistic s : G(n) -greater than R, Ilk, define the mean statistic s as the class function giving the mean of a over. conjugacy classes. We describe a way to calculate the expected value of a on a product of t independently chosen elements from the uniform distribution on a union of conjugacy classes Gamma subset of G(n). In order to apply the formula, one needs to express the class function 3 as a linear combination of irreducible G(n)-characters. We provide such expressions for several commonly studied permutation statistics, including the exceedance number, inversion number, descent number, major index and k-cycle number. In particular, this leads to formulae for the expected values of said statistics.

Place, publisher, year, edition, pages
Elsevier , 2014. Vol. 54, 1-10 p.
Keyword [en]
Symmetric group characters; Random walks; Permutation statistics
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-105898DOI: 10.1016/j.aam.2013.10.003ISI: 000332427700001OAI: diva2:712108
Available from: 2014-04-14 Created: 2014-04-12 Last updated: 2014-04-14

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Hultman, Axel
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Mathematics and Applied MathematicsThe Institute of Technology
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