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 of partition pairs of with -cores by employing elementary -series techniques and certain -dissection formulas. We then discover an infinite family of congruences for as a consequence of these linear identities.
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