Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flag subdivisions and $\gamma$-vectors   The $\gamma$-vector is an important enumerative invariant of a flag
simplicial homology sphere. It has been conjectured by Gal that this vector is
nonnegative for every such sphere $\Delta$ and by Reiner, Postnikov and
Williams that it increases when $\Delta$ is replaced by any flag simplicial
homology sphere which geometrically subdivides $\Delta$. Using the
nonnegativity of the $\gamma$-vector in dimension 3, proved by Davis and Okun,
as well as Stanley's theory of simplicial subdivisions and local $h$-vectors,
the latter conjecture is confirmed in this paper in dimensions 3 and 4.

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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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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: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph