Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shephard's inequalities, Hodge-Riemann relations, and a conjecture of
  Fedotov   A well-known family of determinantal inequalities for mixed volumes of convex
bodies were derived by Shephard from the Alexandrov-Fenchel inequality. The
classic monograph Geometric Inequalities by Burago and Zalgaller states a
conjecture on the validity of higher-order analogues of Shephard's
inequalities, which is attributed to Fedotov. In this note we disprove
Fedotov's conjecture by showing that it contradicts the Hodge-Riemann relations
for simple convex polytopes. Along the way, we make some expository remarks on
the linear algebraic and geometric aspects of these inequalities.

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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: astro-ph