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MiS Preprint
109/2020

Von Staudt Constructions for Skew-Linear and Multilinear Matroids

Lukas Kühne, Rudi Pendavingh and Geva Yashfe

Abstract

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.

Received:
Dec 15, 2020
Published:
Dec 18, 2020
MSC Codes:
05B35, 52B40, 14N20, 52C35, 20F10, 03D40
Keywords:
matroids, characteristic set, word problem

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Preprint
2020 Repository Open Access
Lukas Kühne, Rudi Pendavingh and Geva Yashfe

Von Staudt constructions for skew-linear and multilinear matroids