Stanley's reciprocity theorem

Stanley's reciprocity theorem, named after the mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the integer-point generating function of a rational cone and the generating function of the cone's interior. == Definitions == A rational cone is a subset of R d {\displaystyle {\bf {R}}^{d}} consisting of all points satisfying a finite set of homogeneous linear inequalities with integer coefficients or, alternatively, the nonnegative span of a finite set of integer vectors.

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