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

2017/07/21 by Carrie Rutherford, Robin Whitty, Rutherford, Carrie +1
Computer Science · #05B35 #Advanced Graph Theory Research #Cellular Automata and Applications #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1707.06727

openalex publication_date 2017/07/21 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28

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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