Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operads with compatible CL-shellable partition posets admit a
  Poincar\'e-Birkhoff-Witt basis   In 2007, Vallette built a bridge across posets and operads by proving that an
operad is Koszul if and only if the associated partition posets are
Cohen-Macaulay. Both notions of being Koszul and being Cohen-Macaulay admit
different refinements: our goal here is to link two of these refinements. We
more precisely prove that any (basic-set) operad whose associated posets admit
isomorphism-compatible CL-shellings admits a Poincar\'e-Birkhoff-Witt basis.
Furthermore, we give counter-examples to the converse.

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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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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: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph