## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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Thursday, March 6, 2014 — 1:30 PM EST

Let d and q be positive integers, and consider representing a positive integer n with base d and digits 0, 1, · · · , q − 1. If q < d, then not all positive integers can be represented. If q = d, every positive integer can be represented in exactly one way. If q > d, then there may be multiple ways of representing the integer n. Let fd,q (n) be the number of representations of n with base d and digits 0, 1, · · · , q − 1. For example, if d = 2 and q = 7 we might represent 6 as (110)2 = 1·22 +1·21 +0·20 as well as (102)2 = 1 · 22 + 0 · 21 + 2 · 20. In fact, there are six representations in this case (110)2, (102)2, (30)2, (22)2, (14)2 and (6)2, hence f2,7(6) = 6. In this talk we will discuss the asymptotics of fd,q(n) as n → ∞. This depends in a rather strange way on the Generalized Thue-Morse sequence. While many results are computationally/experimentally true, only partial results are known.

Location

MC - Mathematics & Computer Building

5136B

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

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 Indigenous Initiatives Office.