Expected length of a product of random reflections. (Q2846861)
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scientific article; zbMATH DE number 6204371
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Expected length of a product of random reflections. |
scientific article; zbMATH DE number 6204371 |
Statements
3 September 2013
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random permutations
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random transpositions
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numbers of inversions
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Coxeter groups
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random reflections
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absolute lengths
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Expected length of a product of random reflections. (English)
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The paper provides a formula for the expected number of inversions in a permutation obtained from the identity permutation by \(t\) random -- not necessarily adjacent -- transpositions. This framework is generalized to finite irreducible Coxeter groups belonging to type \(A\), \(B\), \(D\) and \(I\), and an exact expression is obtained for the expected length of a product of \(t\) random reflections. The origin of this research is the study of gene order under random transpositions in computational biology.
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