Jarosław Swaczyna: Generalized densities of subsets of natural numbers and associated ideals

Tuesday, May 19, 2015, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Jarosław Swaczyna (Technical University of Łódź)

Title: Generalized densities of subsets of natural numbers and associated ideals

Abstract:

Let g be a function from natural numbers to non-negative reals. We say that a subset A of naturals has g-density zero, if lim_n |{k∈A: k<n}|/g(n) = 0. It is an easy observation that family of g-density zero sets is an ideal.

I will discuss some properties of ideals obtained this way (among others, I will show that they can be generated using Solecki's submeasures). I will then examine inclusions between ideals obtained for different functions g.

I will also discuss connections between our ideals, "density-like" ideals and Erdos-Ulam ideals. I will present joint results with M. Balcerzak, P. Das and M. Filipczak.

Leave a Reply

Your email address will not be published. Required fields are marked *

Time limit is exhausted. Please reload CAPTCHA.