Comparison of permanental bounds of (0, 1)-matrices

✍ Scribed by Suk-Geun Hwang; Arnold R. Kräuter

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 603 KB
• Volume: 84
• Category: Article
• ISSN: 0166-218X
• DOI: 10.1016/s0166-218x(98)00008-0

✦ Synopsis

Let A be a nonnegative integral n-square matrix with row sums ~1, ,r,,. It is known that per,4 <II:=, r,!i'r' if A is a (0, I)-matrix (Mint, 1963; Brigman, 1973) and also that per..4 d 1 + n:=, (G -I) if A is fully indecomposable (Donald et al., 1984). These two bounds are, in general, uncomparable, cvcn in the cast that A is a fully indccomposablc (0, 1 )-matrix.

In this paper we obtain some comparison test for these bounds with the aid of a function involving the gamma function.