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Experimental Mathematics Seminar

"Probability and Ramsey Theory "

Aaron Robertson, Colgate University

Location:  HILL 705
Date & time: Thursday, 13 April 2017 at 5:00PM -



Time: 5:00 PM
Abstract: We will find a threshold function f(k;r) such that almost all r-colorings of more than f(k;r) consecutive integers admit a monochromatic k-term arithmetic progression while almost no r-colorings do if we have less than f(k;r) consecutive integers. We will then move on to investigate the distribution of the random variable X = number of monochromatic k-term arithmetic progressions in [1,n] under random coloring of each integer. It is known that X tends to a Poisson distribution as k tends to infinity. We investigate what X is for small k.

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