Séminaire Lotharingien de Combinatoire, 78B.82 (2017), 12 pp.
Rafael S. González D'León and Joshua Hallam
Whitney Duals of Geometric Lattices
Abstract.
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.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
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