Infinite strict gammoids
Combinatorics
2013-10-25 v1
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. An independent set is maximal precisely if it admits a linkage 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 to the characterization. We then show that the sets linkable onto the sinks form the bases of a (possibly non-finitary) matroid precisely when the substructure does not occur.
Cite
@article{arxiv.1310.6644,
title = {Infinite strict gammoids},
author = {Hadi Afzali and Hiu-Fai Law and Malte Müller},
journal= {arXiv preprint arXiv:1310.6644},
year = {2013}
}