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50 Years of Fine and Wilf

Jeffrey Shallit ( University of Waterloo )

In 1965, Nathan Jacob Fine and Herbert Saul Wilf published
a paper, "Uniqueness theorems for periodic functions", in the
Proceedings of the American Mathematical Society.  It was largely
ignored for 30 years, but in the last twenty years it has become one
of the most cited papers in combinatorics on words.  In this talk I
will discuss the theorem, give two different proofs, and discuss
several interesting generalizations.  The overall theme is the strong
influence of this paper on subsequent research.



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