Finn Lidbetter, Master’s candidate
David R. Cheriton School of Computer Science
The fundamental problem of additive number theory is to determine whether there exists an integer m such that every nonnegative integer (resp., every sufficiently large nonnegative integer) is the sum of at most m elements of S. If so, we call S an additive basis of order m (resp., an asymptotic additive basis of order m). If such an m exists, we also want to find the smallest such m.
In this talk we will prove some new theorems concerning this fundamental problem in additive number theory, using novel techniques from automata theory and formal languages. As an example of our method, we prove that every natural number > 25 is the sum of at most three natural numbers whose base-2 representation has an equal number of 0’s and 1’s.
This is joint work with Jeffrey Shallit and Jason Bell.
Note: This is a practice talk for DLT18 (Developments in Language Theory) in September, and so the presentation will be around 30 minutes.
200 University Avenue West
Waterloo, ON N2L 3G1