A Remark on a Theorem of M. Hall.

摘要

It is pointed out that in any theorem on the permanents of (0,1)-matrices depending on the hypothesis that the permanent be nonzero (such as the theorem of M. Hall (1948)), this condition can be dropped whenever the number of rows does not exceed any row sum. In fact, if A is an m x n (0,1)-matrix, m - n, and if each row sum of A is greater than or equal to m then PER(A) > 0. (Author)