COMPARISON OF PERMANENTAL BOUNDS OF (0,1)-MATRICES

Let A be a nonnegative integral n-square matrix with row sums r(l),... ,r(n). It is known that per A less than or equal to Pi(i=1)(n), r(i)!( 1/ri) if A is a (0, 1)-matrix (Minc, 1963; Bregman, 1973) and also tha t per A less than or equal to 1 + Pi(i=1)(n) (r(i) - 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 boun ds with the aid of a function involving the gamma function. (C) 1998 E lsevier Science B.V. All rights reserved.