Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallelogram polyominoes, the sandpile model on a complete bipartite
  graph, and a q,t-Narayana polynomial   We classify recurrent configurations of the sandpile model on the complete
bipartite graph K_{m,n} in which one designated vertex is a sink. We present a
bijection from these recurrent configurations to decorated parallelogram
polyominoes whose bounding box is a m*n rectangle. Several special types of
recurrent configurations and their properties via this bijection are examined.
For example, recurrent configurations whose sum of heights is minimal are shown
to correspond to polyominoes of least area. Two other classes of recurrent
configurations are shown to be related to bicomposition matrices, a matrix
analogue of set partitions, and (2+2)-free partially ordered sets.
  A canonical toppling process for recurrent configurations gives rise to a
path within the associated parallelogram polyominoes. This path bounces off the
external edges of the polyomino, and is reminiscent of Haglund's well-known
bounce statistic for Dyck paths. We define a collection of polynomials that we
call q,t-Narayana polynomials, defined to be the generating function of the
bistatistic (area,parabounce) on the set of parallelogram polyominoes, akin to
the (area,hagbounce) bistatistic defined on Dyck paths in Haglund (2003). In
doing so, we have extended a bistatistic of Egge, Haglund, Kremer and
Killpatrick (2003) to the set of parallelogram polyominoes. This is one answer
to their question concerning extensions to other combinatorial objects.
  We conjecture the q,t-Narayana polynomials to be symmetric and prove this
conjecture for numerous special cases. We also show a relationship between
Haglund's (area,hagbounce) statistic on Dyck paths, and our bistatistic
(area,parabounce) on a sub-collection of those parallelogram polyominoes living
in a (n+1)*n rectangle.

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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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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: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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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: solv-int
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: econ