Title: "Independent space of q-polymatroid"

 

Abstract: Matroids and q-matroids can be defined in different ways. Among others, one can define a rank function on the collection of subsets or subspaces, or one can start with a specific collection of subsets or subspaces which satisfy specific properties. In either case one can definition fully determines the other. It has become of interest in algebraic coding theory to study q-polymatroid to get information about some invariants of rank metric codes, which are subspaces of the space of nxm matrices of F_q. Since q-polymatroids are a generalization of q-matroids, it is natural to ask whether independent spaces of q-polymatroids can be defined, and whether they fully determine the q-polymatroid? This talk will answer those questions and provide a definition of independent spaces for q-polymatroid and some of its properties.