Seda Albayrak - Sparse automatic sets in multiplicatively independent bases

jeudi 22 oct. 2026, 15:00 → 16:00 Europe/Paris

112 (ICJ)

Abstract: Cobham’s theorem states that a set of natural numbers recognizable by finite automata in two multiplicatively independent bases is ultimately periodic, or equivalently, definable in Presburger arithmetic. What can we say instead about the intersection of two different sets, each recognizable in one of these bases? We consider this question for sparse automatic sets whose counting functions have polylogarithmic growth. We show that their intersection is finite and give an explicit upper bound on its cardinality in terms of the bases and the sizes of the recognizing automata. We also extend this result to the multidimensional setting. This is joint work with Jason Bell.