Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stanley's nonunimodal Gorenstein h-vector is optimal   We classify all possible $h$-vectors of graded artinian Gorenstein algebras
in socle degree 4 and codimension $\leq 17$, and in socle degree 5 and
codimension $\leq 25$. We obtain as a consequence that the least number of
variables allowing the existence of a nonunimodal Gorenstein $h$-vector is 13
for socle degree 4, and 17 for socle degree 5.
  In particular, the smallest nonunimodal Gorenstein $h$-vector is
$(1,13,12,13,1)$, which was constructed by Stanley in his 1978 seminal paper on
level algebras. This solves a long-standing open question in this area. All of
our results are characteristic free.

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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph