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Thursday, April 14, 2011

Number Theory Seminar
1:00 pm   in 241 Altgeld Hall,  Thursday, April 14, 2011
 Del Edit Copy
Submitted by pppollac.
 Richard Moy (UIUC Math)On the Growth of the Counting Function of Stanley SequencesAbstract: Given a finite set of nonnegative integers A with no three-term arithmetic progressions, the Stanley sequence generated by A, denoted S(A), is the infinite set created by beginning with A and then greedily including strictly larger integers which do not induce a three-term arithmetic progression in S(A). Erdos et al. asked whether the counting function, S(A,x), of a Stanley sequence S(A) satisfies S(A,x)> x^{1/2-epsilon} for every \epsilon > 0 and x > x_0(\epsilon, A). In this talk, we answer this question in the affirmative; in fact, we prove a slightly stronger result.