Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial duality for Poincar\'e series, polytopes and invariants of
  plumbed 3-manifolds   Assume that the link of a complex normal surface singularity is a rational
homology sphere. Then its Seiberg-Witten invariant can be computed as the
`periodic constant' of the topological multivariable Poincar\'e series (zeta
function). This involves a complicated regularization procedure (via
quasipolynomials measuring the asymptotic behaviour of the coefficients).
  We show that the (a Gorenstein type) symmetry of the zeta function combined
with Ehrhart-Macdonald-Stanley reciprocity (of Ehrhart theory of polytopes)
provide a simple expression for the periodic constant. Using these dualities we
also find a multivariable polynomial generalization of the Seiberg-Witten
invariant, and we compute it in terms of lattice points of certain polytopes.
All these invariants are also determined via lattice point counting, in this
way we establish a completely general topological analogue of formulae of
Khovanskii and Morales valid for singularities with non-degenerate Newton
principal part.

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The categories of this paper are: nucl-th
34
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: econ
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: nlin