An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations
Combinatorics
2017-07-24 v1
Abstract
A fundamental theorem of matroid theory establishes that a transversal matroid is representable over fields of any characteristic. It was proved in 1970 by Piff and Welsh: their proof is elegant and concise and, moveover, constructive. However it is far from being algorithmic, in terms of suggesting a step-by-step procedure for deriving a collection of vectors over a given base field representing the transversal matroid induced by a given set system. In this note we recast Piff and Welsh's proof in algorithmic form.
Keywords
Cite
@article{arxiv.1707.06727,
title = {An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations},
author = {Carrie Rutherford and Robin Whitty},
journal= {arXiv preprint arXiv:1707.06727},
year = {2017}
}