## Finding Large Sets Without Arithmetic Progressions of Length Three |

**William Gasarch**

University of Maryland

January 8, 2004

4:30 pm

Bailey Hall 201

What is the largest subset of {1,2,3,...,100000} that does not have ANY arithmetic progressions of length three? (That is, it cannot have 11, 13, 15, or 30, 35, 40, or any set of three numbers that are equally spaced.)There is a large literature on the problem of what is the largest subset of {1,2,...,

n}, but the results are asymptotic---they hold only whennis large.We have combined the literature with computer experiments to find large subsets of {1,2,...,

n} for reasonably sizedn.In this talk we will review the literature, say how we had to modify it for our purposes, and present empirical results.

(William Gasarch will also give a talk in the Computer Science Department. Check out http://cs.union.edu/seminar/gasarch.html for details.)

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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