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On Brylawski’s Generalized Duality

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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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  1. Department of Mathematics, Lafayette College, Easton, PA, 18042-1781, USA

    Gary Gordon

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  1. Gary Gordon
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Correspondence to Gary Gordon.

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Gordon, G. On Brylawski’s Generalized Duality. Math.Comput.Sci. 6, 135–146 (2012). https://doi.org/10.1007/s11786-012-0119-4

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  • DOI: https://doi.org/10.1007/s11786-012-0119-4

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