Obere Schranken für die Permanente von (1,-1)-Matrizen
Séminaire lotharingien de combinatoire, Tome 10 (1984)
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E. T. H. Wang posed the following problem: is there a good upper bound for the permanent of a nonsingular (1,-1)-matrix? We conjecture an upper bound, namely the permanent of the nxn (1,-1)-matrix having exactly (n-1) -1's, these -1's being on the main diagonal, and prove that this upper bound holds for a large class of nonsingular matrices. Another upper bound, weaker than the above, is deduced for the permanents of a large class of (1,-1)-matrices, some of which are singular.
This is a report on the papers:
Arnold R. Kräuter, Norbert Seifter, Some properties of the permanent of (1,-1)-matrices, Linear and Multilinear Algebra 15 (1984), 207-223.
Norbert Seifter, Upper bounds for permanents of (1,-1)-matrices, Israel J. Math. 48 (1984), 69-78.
@article{SLC_1984_10_a6,
author = {Norbert Seifter},
title = {Obere {Schranken} f\"ur die {Permanente} von {(1,-1)-Matrizen}},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {10},
year = {1984},
url = {http://geodesic.mathdoc.fr/item/SLC_1984_10_a6/}
}
Norbert Seifter. Obere Schranken für die Permanente von (1,-1)-Matrizen. Séminaire lotharingien de combinatoire, Tome 10 (1984). http://geodesic.mathdoc.fr/item/SLC_1984_10_a6/