Infinite Gammoids

Seyed Hadi Afzali Borujeni, Hiu-Fai Law, Malte Müller

Abstract


Finite strict gammoids, introduced in the early 1970's, are matroids defined via finite digraphs equipped with some set of sinks: a set of vertices is independent if it admits a linkage to these sinks. In particular, an independent set is maximal (i.e. a base) precisely if it is linkable onto the sinks.

In the infinite setting, this characterization of the maximal independent sets need not hold. We identify a type of substructure as the unique obstruction. This allows us to prove that the sets linkable onto the sinks form the bases of a (possibly non-finitary) matroid if and only if this substructure does not occur.


Keywords


Infinite matroids; strict gammoids; transversal matroid; linkage; infinite digraphs; rays

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