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arXiv · 2408.00630

Representability of the direct sum of uniform q-matroids

Gianira N. Alfarano·Relinde Jurrius·Alessandro Neri·Ferdinando Zullo
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Abstract

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.

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Gianira N. Alfarano, Relinde Jurrius, Alessandro Neri, Ferdinando Zullo. 2024-08-01. Representability of the direct sum of uniform q-matroids. https://arxiv.org/abs/2408.00630

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