Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect Matchings and the Octahedron Recurrence   We study a recurrence defined on a three dimensional lattice and prove that
its values are Laurent polynomials in the initial conditions with all
coefficients equal to one. This recurrence was studied by Propp and by Fomin
and Zelivinsky. Fomin and Zelivinsky were able to prove Laurentness and
conjectured that the coefficients were 1. Our proof establishes a bijection
between the terms of the Laurent polynomial and the perfect matchings of
certain graphs, generalizing the theory of Aztec diamonds. In particular, this
shows that the coefficients of this polynomial, and polynomials obtained by
specializing its variables, are positive, a conjecture of Fomin and Zelevinsky.

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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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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: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org