Geodesic
Whitney Duals of Geometric Lattices
Séminaire lotharingien de combinatoire, 78B (2017) 
Rafael S. González D'León; Joshua Hallam. Whitney Duals of Geometric Lattices. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a81/
@article{SLC_2017_78B_a81,
     author = {Rafael S. Gonz\'alez D'Le\'on and Joshua Hallam},
     title = {Whitney {Duals} of {Geometric} {Lattices}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2017},
     volume = {78B},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a81/}
}
TY  - JOUR
AU  - Rafael S. González D'León
AU  - Joshua Hallam
TI  - Whitney Duals of Geometric Lattices
JO  - Séminaire lotharingien de combinatoire
PY  - 2017
VL  - 78B
UR  - http://geodesic.mathdoc.fr/item/SLC_2017_78B_a81/
ID  - SLC_2017_78B_a81
ER  - 
%0 Journal Article
%A Rafael S. González D'León
%A Joshua Hallam
%T Whitney Duals of Geometric Lattices
%J Séminaire lotharingien de combinatoire
%D 2017
%V 78B
%U http://geodesic.mathdoc.fr/item/SLC_2017_78B_a81/
%F SLC_2017_78B_a81

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Given a graded partially ordered set P, let wk(P) and Wk(P) denote its Whitney numbers of the first and second kind respectively. We call a graded partially ordered set Q a Whitney Dual of P if |wK(P)| = WK(Q) and Wk(P) = |wk(Q)| for all k. In this extended abstract, we show that every geometric lattice has a Whitney dual. This is done constructively, using edge labelings and quotient posets.