Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on a combinatorial interpretation of the e-coefficients of the
  chromatic symmetric function   Stanley has studied a symmetric function generalization X_G of the chromatic
polynomial of a graph G. The innocent-looking Stanley-Stembridge Poset Chain
Conjecture states that the expansion of X_G in terms of elementary symmetric
functions has nonnegative coefficients if G is a clawfree incomparability
graph. Here we give a combinatorial interpretation of these coefficients by
combining Gasharov's work on the conjecture with Egecioglu and Remmel's
combinatorial interpretation of the inverse Kostka matrix. This gives a new
proof of a partial nonnegativity result of Stanley. As an interesting byproduct
we derive a previously unnoticed result relating acyclic orientations to
P-tableaux.

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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin