Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enumerative $g$-theorems for the Veronese construction for formal power
  series and graded algebras   Let $(a_n)_{n \geq 0}$ be a sequence of integers such that its generating
series satisfies $\sum_{n \geq 0} a_nt^n = \frac{h(t)}{(1-t)^d}$ for some
polynomial $h(t)$. For any $r \geq 1$ we study the coefficient sequence of the
numerator polynomial $h_0(a^{<r >}) +...+ h_{\lambda'}(a^{<r >}) t^{\lambda'}$
of the $r$\textsuperscript{th} Veronese series $a^{<r >}(t) = \sum_{n \geq 0}
a_{nr} t^n$. Under mild hypothesis we show that the vector of successive
differences of this sequence up to the $\lfloor \frac{d}{2}
\rfloor$\textsuperscript{th} entry is the $f$-vector of a simplicial complex
for large $r$. In particular, the sequence satisfies the consequences of the
unimodality part of the $g$-conjecture. We give applications of the main result
to Hilbert series of Veronese algebras of standard graded algebras and the
$f$-vectors of edgewise subdivisions of simplicial complexes.

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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph