2022/11/21 by Heide Gluesing-Luerssen, Gluesing-Luerssen, Heide, Benjamin Jany +1
Computer Science · Engineering · #Advanced Graph Theory Research #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2211.11626
openalex publication_date 2022/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
While there are many parallels between matroid theory and q-matroid theory, most notably on the level of cryptomorphisms, there are substantial differences when it comes to the direct sum. The direct sum of q-matroids has been introduced in the literature only recently. In this short note we show that the direct sum of representable q-matroids may not be representable. It remains an open question whether representability of the direct sum can be characterized by the given q-matroids.