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  "body": "\n## Statement\n\nStanley's reciprocity theorem states that for a $d$-dimensional rational cone $C$, we have the following identity of rational functions:\n\n$$F_C(1/x_1,\\dots,1/x_d)=(-1)^d F_{{\\rm int}(C)}(x_1,\\dots,x_d).$$\n\nStanley's reciprocity theorem generalizes Ehrhart-Macdonald reciprocity for Ehrhart polynomials of rational convex polytopes. Both of these results are examples of combinatorial reciprocity theorems, a term that was, in fact, also coined by Stanley.\n",
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