Extension condition for strict gammoids to satisfy the maximality axiom

Let (D,B0)(D,B_0) be a dimaze, and let ML(D,B0)M_L(D,B_0) be its linkability system. For every IML(D,B0)I\in M_L(D,B_0) and every BB0B\subseteq B_0, suppose there is a maximal independent set in IBI\cup B extending II. Extension conjecture. Then the maximality axiom (IM) holds for ML(D,B0)M_L(D,B_0). This proposes a sufficient condition for the linkability system of a strict gammoid to be a matroid; the source gives no resolution of the claim.

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Primary source

Hadi Afzali, Hiu-Fai Law and Malte Müller, “Infinite strict gammoids”, arXiv:1310.6644 (2013).

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