Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generating Functions for Domino Matchings in the $2\times k$ Game of
  Memory   When all the elements of the multiset $\{1,1,2,2,3,3,\ldots,k,k\}$ are placed
in the cells of a $2\times k$ rectangular array, in how many configurations are
exactly $v$ of the pairs directly over top one another, and exactly $h$
directly beside one another --- thus forming $2\times 1$ or $1\times 2$
dominoes? We consider the sum of matching numbers over the graphs obtained by
deleting $h$ horizontal and $v$ vertical vertex pairs from the $2\times k$ grid
graph in all possible ways, providing a generating function for these aggregate
matching polynomials. We use this result to derive a formal generating function
enumerating the domino matchings, making connections with linear chord
diagrams.

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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc