A Normality Conjecture on Rational Base Number Systems

RESUMEN: The rational base number system, introduced by Akiyama, Frougny, and Sakarovitch in 2008, is a generalization of the classical integer base number system. Within this framework two interesting families of infinite words emerge, called minimal and maximal words.

We formulate the conjecture that every minimal and maximal word is normal over an appropriate subalphabet.

The aim of the talk is to convince the audience that the conjecture seems true and of considerable difficulty. In particular, we shall discuss its connections with several older conjectures, including the existence of Z-numbers (Mahler, 1968) and Z_p/q-numbers (Flatto, 1992), the existence of triple expansions in rational base p/q  (Akiyama, 2008), and the Collatz-inspired ‘4/3 problem’ (Dubickas and Mossinghoff, 2009).

Posted on Jan 15, 2026 in Dynamical Systems, Seminars