Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A reciprocity theorem for domino tilings   Let T(m,n) denote the number of ways to tile an m-by-n rectangle with
dominos. For any fixed m, the numbers T(m,n) satisfy a linear recurrence
relation, and so may be extrapolated to negative values of n; these
extrapolated values satisfy the relation T(m,-2-n) = epsilon_{m,n} T(m,n),
where epsilon_{m,n} is -1 if m is congruent to 2 (mod 4) and n is odd, and is
+1 is otherwise. This is equivalent to a fact demonstrated by Stanley using
algebraic methods. Here I give a proof that provides, among other things, a
uniform combinatorial interpretation of T(m,n) that applies regardless of the
sign of n.

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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: dg-ga