A note on the spectra of certain skew-symmetric \(\{1,0,-1\}\)-matrices
The author gives equivalent characterizations of skew-symmetric \(\{1,0,-1\}\) matrices \(A=(a_{xy})\) satisfying the property \(a_{wx}a_{yz}+ a_{wy}a_{zx}+ a_{wz}a_{xy}= a_{wx}a_{wy}a_{wz}a_{xy}a_{xz}a_{yz}\) for all distinct \(x,y,z,w\) in \(\{1,2,\dots,n\}\) related to the Pfaffian of \(A\). As an implication, the author is able to characterize the unimodular orientations of the complete graph, chirotopes of rank 2, and of a class of multipartite oriented graphs.
scientific article; zbMATH DE number 1839040