Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of Labelled Parallelogram polyominoes   We obtain explicit formulas for the enumeration of labelled parallelogram
polyominoes. These are the polyominoes that are bounded, above and below, by
north-east lattice paths going from the origin to a point (k,n). The numbers
from 1 and n (the labels) are bijectively attached to the $n$ north steps of
the above-bounding path, with the condition that they appear in increasing
values along consecutive north steps. We calculate the Frobenius characteristic
of the action of the symmetric group S_n on these labels. All these enumeration
results are refined to take into account the area of these polyominoes. We make
a connection between our enumeration results and the theory of operators for
which the intergral Macdonald polynomials are joint eigenfunctions. We also
explain how these same polyominoes can be used to explicitly construct a linear
basis of a ring of SL_2-invariants.

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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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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: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph