Abstract
Basically there have been two attempts to generalize classical matroids to ordered sets. The first one is the notion of supermatroids introduced by Dunstan, Ingleton and Welsh [1972]. Here the independent sets correspond to nodes in a partially ordered set so that if x is independent, then the whole principal ideal of x consists of independent nodes and for any y, any two maximal independent nodes below y have the same height.
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© 1991 Springer-Verlag Berlin Heidelberg
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Korte, B., Schrader, R., Lovász, L. (1991). Greedoids on Partially Ordered Sets. In: Greedoids. Algorithms and Combinatorics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58191-5_8
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DOI: https://doi.org/10.1007/978-3-642-58191-5_8
Publisher Name: Springer, Berlin, Heidelberg
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