Representability of the Direct Sum of $q$-Matroids
Combinatorics
2023-02-24 v2 Information Theory
math.IT
Abstract
While there are many parallels between matroid theory and -matroid theory, most notably on the level of cryptomorphisms, there are substantial differences when it comes to the direct sum. The direct sum of -matroids has been introduced in the literature only recently. In this short note we show that the direct sum of representable -matroids may not be representable. It remains an open question whether representability of the direct sum can be characterized by the given -matroids.
Cite
@article{arxiv.2211.11626,
title = {Representability of the Direct Sum of $q$-Matroids},
author = {Heide Gluesing-Luerssen and Benjamin Jany},
journal= {arXiv preprint arXiv:2211.11626},
year = {2023}
}