2020/12/14 by Lukas Kühne, Kühne, Lukas, Rudi Pendavingh +3 · 2 citations
Computer Science · Mathematics · #03D40 #05B35 #14N20 #20F10 #52B40 #52C35 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO) #Matrix Theory and Algorithms #Polynomial and algebraic computation #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2012.07361
openalex publication_date 2020/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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: \bullet Undecidability of several matroid representation problems over division rings. \bullet An example of a matroid with an infinite multilinear characteristic set, but which is not multilinear in characteristic 0. \bullet An example of a skew-linear matroid that is not multilinear.