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Perhaps this is too late for your seminar, but there has been a huge literature on these problems and related ones. The key words to search are: "h-vector of...". For example, here is a paper that deals with Gorenstein domains of codimension three. Here is a paper on h-vector of Gorenstein toric ring, which Section 4 of Stanley's paper addressed.

In general, even for Artinian Gorenstein algebras, a complete chracterization of h-vector seems to be out of reach, but there are many surveys and works are being posted at this very momentthis very moment.

Perhaps this is too late for your seminar, but there has been a huge literature on these problems and related ones. The key words to search are: "h-vector of...". For example, here is a paper that deals with Gorenstein domains of codimension three. Here is a paper on h-vector of Gorenstein toric ring, which Section 4 of Stanley's paper addressed.

In general, even for Artinian Gorenstein algebras, a complete chracterization of h-vector seems to be out of reach, but there are many surveys and works are being posted at this very moment.

Perhaps this is too late for your seminar, but there has been a huge literature on these problems and related ones. The key words to search are: "h-vector of...". For example, here is a paper that deals with Gorenstein domains of codimension three. Here is a paper on h-vector of Gorenstein toric ring, which Section 4 of Stanley's paper addressed.

In general, even for Artinian Gorenstein algebras, a complete chracterization of h-vector seems to be out of reach, but there are many surveys and works are being posted at this very moment.

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Hailong Dao
Hailong Dao
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Perhaps this is too late for your seminar, but there has been a huge literature on these problems and related ones. The key words to search are: "h-vector of...". For example, here is a paper that deals with Gorenstein domains of codimension three. Here is a paper on h-vector of Gorenstein toric ring, which Section 4 of Stanley's paper addressed.

In general, even for Artinian Gorenstein algebras, a complete chracterization of h-vector seems to be out of reach, but there are many surveys and works are being posted at this very moment.