Séminaire Lotharingien de Combinatoire, B67e (2012), 20 pp.
Ron M. Adin, Francesco Brenti and Yuval Roichman
Flag Weak Order on Wreath Products
Abstract.
A generating set for the wreath product Zr wreath Sn which leads
to a nicely behaved weak order is presented. It is shown that the
resulting poset has properties analogous to those of the weak
order on the symmetric group: it is a self-dual lattice,
ranked by the Foata-Han flag inversion number; any two maximal
chains are connected via Tits-type pseudo-Coxeter moves; and its
intervals have the desired homotopy types. The associated Möbius
function and relevant generating functions are computed.
Received: October 2, 2011.
Accepted: March 8, 2012.
Final Version: September 24, 2012.
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