Abstract
We introduce a notion of duality—due to Brylawski—that generalizes matroid duality to arbitrary rank functions. This allows us to define a generalization of the matroid Tutte polynomial. This polynomial satisfies a deletion-contraction recursion, where deletion and contraction are defined in this more general setting. We explore this notion of duality for greedoids, antimatroids and demi-matroids, proving that matroids correspond precisely to objects that are simultaneously greedoids and “dual” greedoids.
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