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.
@article{10_37236_4181,
author = {Seyed Hadi Afzali Borujeni and Hiu-Fai Law and Malte M\"uller},
title = {Infinite gammoids},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {1},
doi = {10.37236/4181},
zbl = {1308.05030},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4181/}
}
TY - JOUR
AU - Seyed Hadi Afzali Borujeni
AU - Hiu-Fai Law
AU - Malte Müller
TI - Infinite gammoids
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/4181/
DO - 10.37236/4181
ID - 10_37236_4181
ER -
%0 Journal Article
%A Seyed Hadi Afzali Borujeni
%A Hiu-Fai Law
%A Malte Müller
%T Infinite gammoids
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/4181/
%R 10.37236/4181
%F 10_37236_4181
Seyed Hadi Afzali Borujeni; Hiu-Fai Law; Malte Müller. Infinite gammoids. The electronic journal of combinatorics, Tome 22 (2015) no. 1. doi: 10.37236/4181
