Independent Spaces of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-Polymatroids

This paper is devoted to the study of independent spaces q-polymatroids. With aid an auxiliary q-matroid it shown that collection satisfies same properties as for q-matroids. However, in contrast q-matroids, rank value space does not agree with its dimension. Nonetheless, values fully determine q-polymatroid, and this fact can be exploited derive a cryptomorphism Finally, notions minimal spanning spaces, maximally strongly bases will elaborated on.