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
published in: Journal of pure and applied algebra (2020), pp not yet known
DOI number (of the published article): 10.1016/j.jpaa.2020.106404
Bibtex
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.

Abstract:
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.