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arXiv · 0909.0103

The expected number of inversions after n adjacent transpositions

Mireille Bousquet-Mélou
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Abstract

We give a new expression for the expected number of inversions in the product of n random adjacent transpositions in the symmetric group S_{m+1}. We then derive from this expression the asymptotic behaviour of this number when n scales with m in various ways. Our starting point is an equivalence, due to Eriksson et al., with a problem of weighted walks confined to a triangular area of the plane.

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Mireille Bousquet-Mélou. 2010-03-02. The expected number of inversions after n adjacent transpositions. https://doi.org/10.1016/j.disc.2004.09.015

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