Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gessel polynomials, rooks, and extended Linial arrangements   We study a family of polynomials associated with ascent-descent statistics on
labeled rooted plane k-ary trees introduced by Gessel, from a rook-theoretic
perspective. We generalize the excedance statistic on permutations to maximal
nonattacking rook placements on certain rectangular boards by decomposing them
into boards of staircase shape. We then relate the number of maximal
nonattacking rook placements on certain skew boards to the number of regions in
extended Linial arrangements by establishing a relation between the factorial
polynomial of those boards to the characteristic polynomial of extended Linial
arrangements. Furthermore, we give a combinatorial interpretation of the number
of bounded regions in extended Linial arrangements in the setting of labeled
rooted plane k-ary trees. Finally, using the work of Goldman-Joichi-White, we
identify graphs whose chromatic polynomials equal the characteristic
polynomials of extended Linial arrangements upto a straightforward
normalization.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int