Prof. Eric Rowland from Hofstra University will give the first guest math colloquium talk of the semester on Friday, January 20. His title and abstract are below.
Colloquium meets at 3:30 p.m. in GEM 120. All are welcome, whether you’re registered for colloquium or not.
Title: Avoiding repetitions in sequences of integers
Abstract: Is there an infinite sequence of 0s, 1s, and 2s where no block occurs twice consecutively? Questions like this were investigated a century ago by the Norwegian mathematician Axel Thue, who produced some of the earliest results in an area called “combinatorics on words”. When repetitions of a certain kind are avoidable on a given alphabet, it is natural to ask about the lexicographically least sequence that avoids them. Occasionally the structure of this sequence can be discovered and proved by hand. But for many kinds of repetitions this sequence is sufficiently complex that computer-assisted discovery, followed by automated proofs, seems to be necessary to make any progress.