A lower bound for permanents of (0,1)-matrices

Abstract

Clearly the permanent function is invariant under permutations of rows and columns and under matrix transposition. An up-to-date account of the theory of permanents and an extensive bibliography on the subject is to be found in [2]. The permanent function plays an important part in combinatorics. In fact, the permanent of a (0, 1)-matrix (i.e., a matrix all of whose entries are 0 and 1) is the number of systems of distinct representatives for the corresponding configuration [7, p. 54]. It is therefore of considerable interest to determine the bounds for permanents of (0, 1)-matrices with prescribed row sums (and/or column sums). Let ri and cj denote the ith row sum and the jth column sum of A respectively, i.e.,