Permanent and determinant
This paper gives the bound \(m>\sqrt{2}n-6\sqrt{n}\) as the smallest possible dimension m for which the n-dimensional permanent function might be expressible as an m-dimensional determinant function. The proof uses algebraic geometry studying the singular loci of the permanent and determinant functions. The paper generalizes a well known theorem of \textit{M. Marcus} and \textit{H. Minc} [Illinois J. Math. 5, 376-381 (1961; Zbl 0104.009)].
scientific article; zbMATH DE number 4035986