Title: Szemeredi's Theorem, Stanley Sequences, Erdos, and a Greedy Algorithm
Speaker: Richard Moy
Speaker Info: 1st Year
Brief Description:
Special Note:
Abstract:
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 lightly stronger result. This talk will be accessible to all graduate students.Date: Tuesday, January 31, 2012