This article documents my journey down the rabbit hole, chasing what I have come to know as a particularly unyielding problem in Ramsey theory on the integers: the -large conjecture. This conjecture states that if has the property that every -coloring of admits arbitrarily long monochromatic arithmetic progressions with common difference from , then the same property holds for any finite number of colors. We hope to provide a roadmap for future researchers and also provide some new results related to the -large conjecture.
"Down the large rabbit hole." Rocky Mountain J. Math. 50 (1) 237 - 253, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.237