2024/12/17 by Gianira N. Alfarano, Alfarano, Gianira N., Eimear Byrne +3 · 2 citations
Computer Science · Engineering · #Advanced Algebra and Logic #graph theory and CDMA systems #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2412.13025
We introduce the notion of the free product of q-matroids, which is the q-analogue of the free product of matroids. We study the properties of this noncommutative binary operation, making an extensive use of the theory of cyclic flats. We show that the free product of two q-matroids M1 and M2 is maximal with respect to the weak order on q-matroids having M1 as a restriction and M2 as the complementary contraction. We characterise q-matroids that are irreducible with respect to the free product and we prove that the factorization of a q-matroid into a free product of irreducibles is unique up to isomorphism. We discuss the representability of the free product, with a particular focus on rank one uniform q-matroids and show that such a product is represented by clubs on the projective line.