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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