2024/08/01 by Alfarano, Gianira N., Jurrius, Relinde, Neri, Alessandro +1 · 2 citations
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2408.00630
There are many similarities between the theories of matroids and q-matroids. However, when dealing with the direct sum of q-matroids many differences arise. Most notably, it has recently been shown that the direct sum of representable q-matroids is not necessarily representable. In this work, we focus on the direct sum of uniform q-matroids. Using algebraic and geometric tools, together with the notion of cyclic flats of q-matroids, we show that this is always representable, by providing a representation over a sufficiently large field.