Title:Coloring the integers while avoiding monochromatic arithmetic progressions
| Speaker | Torin Greenwood |
| Affiliation | North Dakota State University |
| Location | MC 5479 |
Abstract: Consider coloring the positive integers either red or blue one at a time in order. Van der Waerden's classical theorem states that no matter how you color the integers, you will eventually have k equally spaced integers all colored the same for any k. But, how can we minimize the number of times k equally spaced integers are colored the same? Even for k = 3, this question is unsolved. We will discuss progress towards proving an existing conjecture by leveraging a connection to coloring the continuous interval [0,1]. Our strategy relies on identifying classes of colorings with permutations and then using mixed integer linear programming. Joint work with Jonathan Kariv and Noah Williams.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm,