Von Staudt constructions for skew-linear and multilinear matroids

Lukas Kühne; Rudi Pendavingh; Geva Yashfe

doi:10.5070/C63160429

Von Staudt constructions for skew-linear and multilinear matroids

Lukas Kühne, Rudi Pendavingh, Geva Yashfe

Combinatorial Optimization

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

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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.

Originele taal-2	Engels
Artikelnummer	#16
Aantal pagina's	27
Tijdschrift	Combinatorial Theory
Volume	3
Nummer van het tijdschrift	1
DOI's	https://doi.org/10.5070/C63160429
Status	Gepubliceerd - 2023

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∗Supported by a Minerva fellowship of the Max-Planck-Society, the Studienstiftung des deutschen Volkes and by ERC StG 716424 - CASe. †Supported by ERC StG 716424 - CASe and by ISF grant 1050/16.

Financiers	Financiernummer
Syracuse University
European Research Council	716424
Israel Science Foundation	1050/16
German National Merit Foundation (Studienstiftung des deutschen Volkes)

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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.",

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Von Staudt constructions for skew-linear and multilinear matroids

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