Lecture 1 . Enumerative Combinatorics (Federico Ardila)

Much of enumerative combinatorics concerns the question: “Count the number a_n of elements of a set S_n for n=1,2,...“ We discuss four types of answers: an exact formula, a recursive formula, a formula for the generating function, and an asymptotic formula. We illustrate these four answers by counting the domino tilings of a 2 x n rectangle. Lecture notes at: San Francisco State University (San Francisco, USA) Universidad de Los Andes (Bogota, Colombia) Fall 2013