An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations

Carrie Rutherford; Robin Whitty

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arXiv · 1707.06727

An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations

Carrie Rutherford·Robin Whitty

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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.

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Carrie Rutherford, Robin Whitty. 2017-07-21. An Algorithmic Proof of the Piff--Welsh Theorem on Transversal Matroid Representations. https://arxiv.org/abs/1707.06727

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