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SUMMARY:Seda Albayrak - Sparse automatic sets in multiplicatively independ
 ent bases
DTSTART:20261022T130000Z
DTEND:20261022T140000Z
DTSTAMP:20261030T005000Z
UID:indico-event-17568@indico.math.cnrs.fr
DESCRIPTION:Abstract: Cobham’s theorem states that a set of natural numb
 ers recognizable by finite automata in two multiplicatively independent ba
 ses is ultimately periodic\, or equivalently\, definable in Presburger ari
 thmetic. What can we say instead about the intersection of two different s
 ets\, each recognizable in one of these bases? We consider this question f
 or sparse automatic sets whose counting functions have polylogarithmic gro
 wth. 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 recogn
 izing automata. We also extend this result to the multidimensional setting
 . This is joint work with Jason Bell.\n\nhttps://indico.math.cnrs.fr/event
 /17568/
LOCATION:112 (ICJ)
URL:https://indico.math.cnrs.fr/event/17568/
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