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Combinatorial Derived Matroids
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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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en
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7
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Electronic Journal of Combinatorics, Volume 30, issue 2, pp. 2-8
Abstract
Let M be an arbitrary matroid with circuits C(M). We propose a definition of a derived matroid δM that has as its ground set C(M). Unlike previous attempts of such a definition, our definition applies to arbitrary matroids, and is completely combinatorial. We prove that the rank of δM is bounded from above by |M| −r(M) and that it is connected if and only if M is connected. We compute examples including the derived matroids of uniform matroids, the Vámos matroid and the graphical matroid M(K4). We formulate conjectures relating our construction to previous definitions of derived matroids.
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Publisher Copyright: © The authors. Released under the CC BY license (International 4.0).
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Freij-Hollanti, R, Jurrius, R & Kuznetsova, O 2023, 'Combinatorial Derived Matroids', Electronic Journal of Combinatorics, vol. 30, no. 2, pp. 2-8. https://doi.org/10.37236/11327