Comparison of permanental bounds of (0, 1)-matrices Original Research Article

Let A be a nonnegative integral n-square matrix with row sums r1, …, rn. It is known that perA ⩽ Πni=1ri!lri if A is a (0, 1)-matrix (Minc, 1963; Bregman, 1973) and also that perA ⩽ 1 + Πni = 1 (ri − 1) if A is fully indecomposable (Donald et al., 1984). These two bounds are, in general, uncomparable, even in the case that A is a fully indecomposable (0, 1)-matrix. In this paper we obtain some comparison test for these bounds with the aid of a function involving the gamma function.