坡矩阵的积和式(英文)

The Permanent of an Incline Matrix

在坡上讨论研究矩阵积和式的三类问题:首先,证明当Per(A)=1时,矩阵A的行与列的元素是互补的,同时给出矩阵A可逆的条件;其次,讨论积和式Per(A)与Per(AB)及Per(A+B)间的不等关系,给出若干不等式;最后,研究给出矩阵积和式Per(A)的若干分解.这些结果推广了分配格和交换坡上的相应的结论.

In this paper,three main problems on permanents of incline matrices are discussed.First,we prove that the rows and columns of matrix A are mutual complement when Per(A) = 1.Thus a necessary and sufficient condition is given for a matrix A with Per(A) = 1 to be invertible.Second,the relations among Per(A),Per(AB) and Per(A + B) are investigated.Third,a decomposition is given for Per(A).These results can be regarded as the generalizations of the previous results on the permanents of matrices over distributive lattice and commutative incline.