Bounds on Arithmetic Rainbow Ramsey Multiplicities
Abstract
We study a quantitative Ramsey-type problem on 3-term arithmetic progressions: how should the set of integers [n] = {1, 2, ..., n}$ be colored using 3 colors in order to maximize the number of rainbow 3-term arithmetic progressions? By rainbow, we mean progressions whose elements are each assigned a distinct color. We determine a lower bound for this question and upper and lower bounds when [n] is replaced with the integers modulo n, including an exact maximum when n is a multiple of 3.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- The PUMP Journal of Undergraduate Research
- Volume
- 9
- Pages
- 325–335
- Publication date
- 1 September 2026