Original Paper

Annals of Combinatorics

, Volume 9, Issue 1, pp 21-33

First online:

Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

  • Niklas EriksenAffiliated withDepartment of Mathematics, Royal Institute of Technology Email author 
  • , Axel HultmanAffiliated withFachbereich Mathematik und Informatik, Philipps-Universität Marburg

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Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.

AMS Subject Classification.

05C12 82B41 51F15


complex reflection groups reflection distances random walks