Critical exponent of infinite balanced words via the Pell number system

Aseem Raj Baranwal; Jeffrey Shallit

doi:10.1007/978-3-030-28796-2_6

paper

Critical exponent of infinite balanced words via the Pell number system

arXiv:1902.00503 · doi:10.1007/978-3-030-28796-2_6

Abstract

In a recent paper of Rampersad et al., the authors conjectured that the smallest possible critical exponent of an infinite balanced word over a 5-letter alphabet is $3/2$ . We prove this result, using a formulation of first-order logic, the Pell number system, and a machine computation based on finite-state automata.

14 pages