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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
*w*_{k}(*P*) and
*W*_{k}(*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
|*w*_{K}(*P*)| =
*W*_{K}(*Q*) and
*W*_{k}(*P*) =
|*w*_{k}(*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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