Von Staudt Constructions for Skew-Linear and Multilinear Matroids

Lukas Kühne, Rudi Pendavingh, Geva Yashfe

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This paper compares skew-linear and multilinear matroid representations. These
are matroids that are representable over division rings and (roughly speaking) invertible matrices, respectively. The main tool is the von Staudt construction, by which we translate
our problems to algebra. After giving an exposition of a simple variant of the von Staudt
construction we present the following results:
• Undecidability of several matroid representation problems over division rings.
• An example of a matroid with an infinite multilinear characteristic set, but which is not
multilinear in characteristic 0.
• An example of a skew-linear matroid that is not multilinear.
Original languageEnglish
Article number2012.0736
Publication statusPublished - 14 Dec 2020


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