English

Linear identities for partition pairs with $4$-cores

Number Theory 2026-02-11 v2 Combinatorics

Abstract

We determine an infinite family of linear identities for the number A4(n)A_4(n) of partition pairs of nn with 44-cores by employing elementary qq-series techniques and certain 33-dissection formulas. We then discover an infinite family of congruences for A4(n)A_4(n) as a consequence of these linear identities.

Keywords

Cite

@article{arxiv.2601.10438,
  title  = {Linear identities for partition pairs with $4$-cores},
  author = {Russelle Guadalupe},
  journal= {arXiv preprint arXiv:2601.10438},
  year   = {2026}
}

Comments

Theorem 1.2 has been revised; 14 pages, comments are welcome

R2 v1 2026-07-01T09:05:57.359Z