Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $e$-positivity and Schur positivity of the chromatic symmetric
  functions of some trees   We investigate the $e$-positivity and Schur positivity of the chromatic
symmetric functions of some spider graphs with three legs. We obtain the
positivity classification of all broom graphs and that of most double broom
graphs. The methods involve extracting particular $e$-coefficients of the
chromatic symmetric function of these graphs with the aid of Orellana and
Scott's triple-deletion property, and using the combinatorial formula of Schur
coefficients by examining certain special rim hook tabloids. We also propose
some conjectures on the $e$-positivity and Schur positivity of trees.

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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga