On minimal Gorenstein Hilbert functions

On minimal Gorenstein Hilbert functions

We conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing codimension and length. We prove the conjecture in length four and five, in low codimension. We also prove the conjecture for a particular subclass of algebras...

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Veröffentlicht in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2024, Vol.118 (1), Article 29
Hauptverfasser: Bezerra, Lenin, Gondim, Rodrigo, Ilardi, Giovanna, Zappalà, Giuseppe
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Sprache:eng
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Algebra
Applications of Mathematics
Asymptotic properties
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
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container_title Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas
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Gondim, Rodrigo
Ilardi, Giovanna
Zappalà, Giuseppe
description We conjecture that a class of Artinian Gorenstein Hilbert algebras called full Perazzo algebras always have minimal Hilbert function, fixing codimension and length. We prove the conjecture in length four and five, in low codimension. We also prove the conjecture for a particular subclass of algebras that occurs in every length and certain codimensions. As a consequence of our methods we give a new proof of part of a known result about the asymptotic behavior of the minimum entry of a Gorenstein Hilbert function.
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subjects Algebra
Applications of Mathematics
Asymptotic properties
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Theoretical
title On minimal Gorenstein Hilbert functions
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