论文标题
图形矩阵空间中的最大广义等级
Maximal Generalized Rank in Graphical Matrix Spaces
论文作者
论文摘要
在本说明中，我们证明了由于Li，Qiao，Qiao，Wigderson，Wigderson和Zhang（Arxiv：2206.04815）的最大组合表征的两次扩展，这是图形矩阵空间的最大级别秩下空间的最大维度。我们的第一个结果表明，上述特征对于包括例如永久等级。我们的第二个结果将表征扩展到与一般图相关联的图形交替矩阵空间的有界等级子空间。
In this note we prove two extensions of a recent combinatorial characterization due to Li, Qiao, Wigderson, Wigderson and Zhang (arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the graphical matrix space associated with a bipartite graph. Our first result shows that the above characterization remains valid for a wide class of generalized rank functions, including e.g. the permanental rank. Our second result extends the characterization to bounded rank subspaces of the graphical alternating matrix space associated with a general graph.
