Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting chains in the noncrossing partition lattice via the W-Laplacian   We give an elementary, case-free, Coxeter-theoretic derivation of the formula
$h^nn!/|W|$ for the number of maximal chains in the noncrossing partition
lattice $NC(W)$ of a real reflection group $W$. Our proof proceeds by comparing
the Deligne-Reading recursion with a parabolic recursion for the characteristic
polynomial of the $W$-Laplacian matrix considered in our previous work. We
further discuss the consequences of this formula for the geometric group theory
of spherical and affine Artin groups.

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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin