Congruence Modulo 4 for Andrews’ Even Parts Below Odd Parts Partition Function

Abstract

We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of \(\overline{\mathcal{E}\mathcal{O}}(n)\) and further prove that \(\overline{\mathcal{E}\mathcal{O}}(n)\equiv 0\pmod 4\) for almost all n. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.