Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $e$-positivity of vertical strip LLT polynomials   In this article we prove the $e$-positivity of $G_{\mathbf{\nu}}[X;q+1]$ when
$G_{\mathbf{\nu}}[X;q]$ is a vertical strip LLT polynomial. This property has
been conjectured by Alexandersson and Panova, and by Garsia, Haglund, Qiu and
Romero, and it implies several $e$-positivities conjectured by them and also by
Bergeron.
  We make use of a result of Carlsson and Mellit that shows that a vertical
strip LLT polynomial can be obtained by applying certain compositions of
operators of the Dyck path algebra to the constant $1$. Our proof gives in fact
an algorithm to expand these symmetric functions in the elementary basis, and
it shows, as a byproduct, that these compositions of operators are actually
multiplication operators.

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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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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: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th