Geodesic
A Comparison of Two Upper Bounds for the Permanent of (0,1)-Matrices
Séminaire lotharingien de combinatoire, Tome 36 (1996)

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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. 

@article{SLC_1996_36_a8,
     author = {S.-G. Hwang and A. R. Kr\"auter},
     title = {A {Comparison} of {Two} {Upper} {Bounds} for the {Permanent} of {(0,1)-Matrices}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {36},
     year = {1996},
     url = {http://geodesic.mathdoc.fr/item/SLC_1996_36_a8/}
}
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S.-G. Hwang; A. R. Kräuter. A Comparison of Two Upper Bounds for the Permanent of (0,1)-Matrices. Séminaire lotharingien de combinatoire, Tome 36 (1996). http://geodesic.mathdoc.fr/item/SLC_1996_36_a8/