Linear identities for partition pairs with $5$-cores

Russelle Guadalupe

Linear identities for partition pairs with $5$-cores

Number Theory 2026-01-16 v2 Combinatorics

Authors: Russelle Guadalupe

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.

Keywords

partition congruences partition theory

Cite

@article{arxiv.2601.04743,
  title  = {Linear identities for partition pairs with $5$-cores},
  author = {Russelle Guadalupe},
  journal= {arXiv preprint arXiv:2601.04743},
  year   = {2026}
}

Comments

11 pages, comments welcome

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