This paper is devoted to the study of independent spaces of q-polymatroids. With the aid of an auxiliary q-matroid it is shown that the collection of independent spaces satisfies the same properties as for q-matroids. However, in contrast to q-matroids, the rank value of an independent space does not agree with its dimension. Nonetheless, the rank values of the independent spaces fully determine the q-polymatroid, and this fact can be exploited to derive a cryptomorphism of q-polymatroids. Finally, the notions of minimal spanning spaces, maximally strongly independent spaces, and bases will be elaborated on.
翻译：本文专门论述对q-pollymatroid独立空间的研究,在辅助q-matroid的帮助下,可以证明独立空间的收集与q-matroid具有相同的特性,然而,与q-matroid相比,独立空间的等级价值与它的维度不同,然而,独立空间的等级价值完全决定了q-polymatroid,这一事实可以被利用来得出q-polymatroid的隐性。最后,将阐述最小空间、高度独立的空间和基地的概念。
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