Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unimodal Gorenstein h-vectors without the Stanley-Iarrobino property   The study of the $h$-vectors of graded Gorenstein algebras is an important
topic in combinatorial commutative algebra, which despite the large amount of
literature produced during the last several years, still presents many
interesting open questions. In this note, we commence a study of those unimodal
Gorenstein $h$-vectors that do \emph{not} satisfy the Stanley-Iarrobino
property. Our main results, which are characteristic free, show that such
$h$-vectors exist: 1) In socle degree $e$ if and only if $e\ge 6$; and 2) In
every codimension five or greater. The main case that remains open is that of
codimension four, where no Gorenstein $h$-vector is known without the
Stanley-Iarrobino property. We conclude by proposing the following very general
conjecture: The existence of any arbitrary level $h$-vector is
\emph{independent} of the characteristic of the base field.

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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat