.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.
ON MINIMAL GORENSTEIN HILBERT FUNCTIONS / Bezerra, Lenin; Gondim, Rodrigo; Ilardi, Giovanna; GIUSEPPE ZAPPALÀ, And. - In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS. - ISSN 1579-1505. - 118:29:29(2024). [10.1007/s13398-023-01523-6]
ON MINIMAL GORENSTEIN HILBERT FUNCTIONS
GIOVANNA ILARDI
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2024
Abstract
.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.| File | Dimensione | Formato | |
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