CombinatorialReciprocity

These are notes for a talk I gave on Combinatorial Reciprocity Theorems. These theorems give combinatorial significance to counting functions evaluated at negative integers; they are surprising and quite beautiful. This talk concerned the first few pages of Richard Stanley's landmark 1974 paper "Combinatorial Reciprocity Theorems." The exposition follows the style of Beck and Sanyal's textbook on the subject: Combinatorial Reciprocity Theorems (An Invitation to Enumerative Geometric Combinatorics).