3 problems

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Full Perazzo conjecture on minimal Hilbert vectors
A standard graded Artinian Gorenstein algebra over a characteristic-zero field has a symmetric Hilbert vector. Let $\mathcal{AG}_{st,\mathbb{K}}(n,d)$ denote the poset of Hilbert v…
Conjectureopenartinian-gorenstein-algebras hilbert-vectors perazzo-algebrasarXiv posted 2 days ago
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Minimality conjecture for the Hilbert vectors of full Perazzo algebras
Minimality conjecture for full Perazzo algebras. The $h$ -vectors of full Perazzo algebras are minimal among the $h$ -vectors of all Artinian Gorenstein algebras with the same degree…
Conjectureopenartinian-gorenstein-algebras hilbert-functions perazzo-algebrasarXiv posted 2 days ago
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The strong full Perazzo conjecture for strongly minimal Hilbert functions
The strong full Perazzo conjecture. The Hilbert vector $H$ is strongly minimal in $\mathcal{AG}(r,d)$ .
Conjectureopenartinian-gorenstein-algebras hilbert-functions perazzo-algebrasarXiv posted 2 days ago

Full Perazzo conjecture on minimal Hilbert vectors