Georgia Institute of Technology College of Sciences

Motivated by mass-spectrometry protein sequencing, we consider the simple problem of reconstructing a string from its substring compositions. Relating the question to the long-standing turnpike problem, polynomial factorization, and cyclotomic polynomials, we cleanly characterize the lengths of reconstructable strings and the structure of non-reconstructable ones. The talk is elementary and self contained and covers work with Jayadev Acharya, Hirakendu Das, Olgica Milenkovic, and Shengjun Pan.