## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Wednesday, September 30, 2020 — 2:30 PM EDT

**Seda Albayrak, Department of Pure Mathematics, University of Waterloo**

"A Strong version of Cobham’s theorem"

Cobham’s theorem is a fundamental result in the theory of automatic sequences. It says that if a sequence is both p- and q-automatic with p and q multiplicatively independent integers that are each at least two, then this sequence is ultimately periodic. Using automatic sequences, one can define automatic sets. A long-known dichotomy for the growth of automatic sets says that they are either sparse (growth function is poly-logarithmically bounded) or non-sparse. We consider sparse automatic sets and show that if S is a sparse p-automatic set and T is a sparse q-automatic set with p and q multiplicatively independent integers that are greater than or equal to two, then the intersection of S and T is finite. In fact, we can find an explicit bound for the cardinality of the intersection in terms of the sizes of the automata that accept the sets S and T.

Zoom meeting: https://us02web.zoom.us/j/87636005367?pwd=T2p6ZkJlSUp1d093K3d6NkhFZEVJdz09

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.