Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Computational complexity, Newton polytopes, and Schubert polynomials   The nonvanishing problem asks if a coefficient of a polynomial is nonzero.
Many families of polynomials in algebraic combinatorics admit combinatorial
counting rules and simultaneously enjoy having saturated Newton polytopes
(SNP). Thereby, in amenable cases, nonvanishing is in the complexity class
$NP\cap coNP$ of problems with "good characterizations". This suggests a new
algebraic combinatorics viewpoint on complexity theory.
  This report discusses the case of Schubert polynomials. These form a basis of
all polynomials and appear in the study of cohomology rings of flag manifolds.
We give a tableau criterion for nonvanishing, from which we deduce the first
polynomial time algorithm. These results are obtained from new
characterizations of the Schubitope, a generalization of the permutahedron
defined for any subset of the n x n grid, together with a theorem of A. Fink,
K. M\'{e}sz\'{a}ros, and A. St. Dizier, which proved a conjecture of C.
Monical, N. Tokcan, and the third author.

10
The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph