Circulant matrices and Galois-Togliatti systems
Pietro De Poi, Emilia Mezzetti, Mateusz Michałek, Rosa Maria Miró-Roig, and Eran Nevo
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Submission date: 28. Aug. 2018
MSC-Numbers: 15B05, 15A05, 13E10, 14M25
Keywords and phrases: Circulant matrix, permanent, weak Lefschetz property, Laplace equations, Togliatti systems, monomial ideals
Link to arXiv:See the arXiv entry of this preprint.
The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we prove a conjecture concerning the minimality of Galois-Togliatti systems.