Linear identities for partition pairs with $5$-cores
Abstract
We prove an infinite family of linear identities for the number $A_5(n)$ of partition pairs of $n$ with $5$-cores by using certain theta function identities involving the Ramanujan's parameter $k(q)$ due to Cooper, and Lee and Park. Consequently, we deduce an infinite family of congruences for $A_5(n)$ using these linear identities.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 8 January 2026
- Document type
- Preprint