Geodesic
Flag Weak Order on Wreath Products
Séminaire lotharingien de combinatoire, Tome 67 (2012-2015)
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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. 

@article{SLC_2012-2015_67_a4,
     author = {Ron M. Adin and Francesco Brenti and Yuval Roichman},
     title = {Flag {Weak} {Order} on {Wreath} {Products}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2012-2015},
     volume = {67},
     url = {http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a4/}
}
TY  - JOUR
AU  - Ron M. Adin
AU  - Francesco Brenti
AU  - Yuval Roichman
TI  - Flag Weak Order on Wreath Products
JO  - Séminaire lotharingien de combinatoire
PY  - 2012-2015
VL  - 67
UR  - http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a4/
ID  - SLC_2012-2015_67_a4
ER  - 
%0 Journal Article
%A Ron M. Adin
%A Francesco Brenti
%A Yuval Roichman
%T Flag Weak Order on Wreath Products
%J Séminaire lotharingien de combinatoire
%D 2012-2015
%V 67
%U http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a4/
%F SLC_2012-2015_67_a4
Ron M. Adin; Francesco Brenti; Yuval Roichman. Flag Weak Order on Wreath Products. Séminaire lotharingien de combinatoire, Tome 67 (2012-2015). http://geodesic.mathdoc.fr/item/SLC_2012-2015_67_a4/