Stanley's Reciprocity Theorem

Stanley's reciprocity theorem, named for Richard P. Stanley, is a functional equation relating the generating function that counts integer points in a rational cone to the generating function counting integer points in the cone's interior. Both generating functions are rational functions, and Stanley's theorem shows how they relate through a reciprocity identity; the result generalizes Ehrhart-Macdonald reciprocity for Ehrhart polynomials of rational convex polytopes, and Stanley classified both as examples of what he called combinatorial reciprocity theorems in his foundational 1974 work on the subject. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/