We consider the problem of determining which matrices are permutable to be supmodular. We show that for small dimensions any matrix is permutable by a universal permutation or by a pair of permutations, while for higher dimensions no universal permutation exists. We raise several questions including to determine the dimensions in which every matrix is permutable.

翻译：我们考虑确定哪些矩阵可通过置换变为超模矩阵的问题。我们证明，对于小维数，任意矩阵均可通过通用置换或一对置换实现置换，而对于较高维数，则不存在通用置换。我们提出若干问题，包括确定所有矩阵均可置换的维数。