Séminaire Lotharingien de Combinatoire, 82B.57 (2019), 12 pp.
Joel Brewster Lewis and Alejandro H. Morales
Factorization problems in complex reflection groups
Abstract.
We enumerate factorizations of a Coxeter element into arbitrary factors in the complex reflection groups G(d,1,n) (the wreath product of the symmetric group with a cyclic group) and its subgroup G(d,d,n), applying combinatorial and algebraic methods, respectively. After a change of basis, the coefficients that appear are the same as those that appear in the corresponding enumeration in the symmetric group.
Received: November 15, 2018.
Accepted: February 17, 2019.
Final version: April 1, 2019.
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