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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