Representability of the direct sum of uniform q-matroids
Combinatorics
2026-03-11 v3
Abstract
There are many similarities between the theories of matroids and -matroids. However, when dealing with the direct sum of -matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable -matroids is not necessarily representable. In this work, we focus on the direct sum of uniform -matroids. Using algebraic and geometric tools, together with the notion of cyclic flats of -matroids, we show that this is always representable, by providing a representation over a sufficiently large field.
Keywords
Cite
@article{arxiv.2408.00630,
title = {Representability of the direct sum of uniform q-matroids},
author = {Gianira N. Alfarano and Relinde Jurrius and Alessandro Neri and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2408.00630},
year = {2026}
}