The research findings have been accepted for publication in the Journal of Number Theory.
Overview Link to heading
This project investigates congruence relations for colored partitions of integers. We explore congruences of the form pr(mn + t) ≡ 0 (mod p) for all n, where pr(n) represents the number of r-colored partitions of n and p, m are distinct primes. We discuss the background of Ramanujan’s congruences and the interest they sparked among number theorists. We then introduce theta-type congruences, which are nontrivial congruences that do not follow from Ramanujan-type congruences and provide examples and remarks to illustrate their findings.
Contributions Link to heading
- Played a crucial role in the investigation of congruence relations for colored partitions of integers.
- Explored the background of Ramanujan’s congruences and introduced theta-type congruences as nontrivial congruences.
- Utilized Mathematica for the generation of numerical data, with a specific focus on the case with even R’s.
- Demonstrated a deep understanding of mathematical principles and identified interesting congruences within the data.
- Actively participated in group meetings with colleagues Jamie and Maddie, explaining technical procedures implemented in Mathematica to ensure clear communication and alignment within the team.
Achievements Link to heading
- Enriched mathematical knowledge through active participation in the IGL project.
- Developed important skills such as teamwork, communication, and technical proficiency.
- Contributed to a paper detailing the investigation of congruence relations for colored partitions of integers, which has been accepted for publication in the prestigious Journal of Number Theory.