Expected length of a product of random reflections

Details Expected length of a product of random reflections Expected length of a product of random reflections

2010-11-24

arxiv.org/abs/1011.5358v1

Mathematics

Combinatorics

11 pages

Scientific paper

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 general, 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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