Primitive and geometric-progression-free sets without large gaps.

Event time: 
Wednesday, July 17, 2019 - 2:00pm
LOM 206
Nathan McNew
Speaker affiliation: 
Event description: 

Abstract: A set of integers is primitive if no integer in the set divides another.  The prime numbers form one such a set, but there are many others.  A set is geometric-progression-free if it contains no three terms of the form {a,ar,ar^2}.  We will discuss various “large” primitive and geometric progression free sets and then use the probabilistic method to construct infinite sets which are primitive (or geometric progression free) with relatively small gaps between consecutive terms, substantially smaller than is known to hold for the primes.