Permanent and determinant
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)].
- University of Toronto Canada
Numerical Analysis, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), determinant function, Determinants, permanents, traces, other special matrix functions, singular locus, dimension, p-complete, Discrete Mathematics and Combinatorics, permanent function, Geometry and Topology
Numerical Analysis, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), determinant function, Determinants, permanents, traces, other special matrix functions, singular locus, dimension, p-complete, Discrete Mathematics and Combinatorics, permanent function, Geometry and Topology
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