Growth rate of binary words avoiding xxxR

Abstract

Abstract Consider the set of those binary words with no non-empty factors of the form xxx^R. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this paper, we demonstrate the existence of upper and lower bounds of the form n^{lg n+o(lg n)} on the number of such words of length n, where lg n denotes the base-2 logarithm of n.