2023/02/04 by Heide Gluesing-Luerssen, Gluesing-Luerssen, Heide, Benjamin Jany +1 · 2 citations
Computer Science · Engineering · #Advanced Graph Theory Research #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.2302.02260
openalex publication_date 2023/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the direct sum of q-matroids by way of their cyclic flats. Using that the rank function of a q-matroid is fully determined by the cyclic flats and their ranks, we show that the cyclic flats of the direct sum of two q-matroids are exactly all the direct sums of the cyclic flats of the two summands. This simplifies the rank function of the direct sum significantly. A q-matroid is called irreducible if it cannot be written as a (non-trivial) direct sum. We provide a characterization of irreducibility in terms of the cyclic flats and show that every q-matroid can be decomposed into a direct sum of irreducible q-matroids, which are unique up to equivalence.