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Séminaire Lotharingien de Combinatoire, B36z (1996), 10pp.

# S.-G. Hwang and A. R. Kräuter

# A Comparison of Two Upper Bounds
for the Permanent of (0,1)-Matrices

**Abstract.**
The permanental bounds for (0,1)-matrices by
Minc-Bregman (1973) and for fully indecomposable integral matrices by Donald
* et al.* (1984) are, in general, not comparable, even if we restrict
ourselves to the class of fully indecomposable (0,1)-matrices *A*.
In this note we present sufficient conditions (in terms of the number of
those row sums of *A* that equal 2) such that it is possible to
predict immediately
which of the two bounds yields the better estimation for a given *A*. It is
noteworthy that this can be done without computing the bounds explicitly. As
an important tool we derive a couple of properties of a function that is
closely related to the classical gamma function.

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