2024/08/13 by Degen, Sebastian, Kühne, Lukas
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2408.06795
A q-matroid is the analogue of a matroid which arises by replacing the finite ground set of a matroid with a finite-dimensional vector space over a finite field. These q-matroids are motivated by coding theory as the representable q-matroids are the ones that stem from rank-metric codes. In this note, we establish a q-analogue of Nelson's theorem in matroid theory by proving that asymptotically almost all q-matroids are not representable. This answers a question about representable q-matroids by Jurrius and Pellikaan strongly in the negative.