Let A be a set of nonnegative integers containing 0. There is a unique set B of nonnegative integers such that every positive integer k can be written in an even number of ways in the form a+b, with a in A and b in B. I will discuss the density of the set B for a few specific examples of sets A, including the set of squares, the Thue-Morse numbers, and a random set. This is joint work with J. Cooper and D. Eichhorn.
Kevin O'Bryant