2021•arXiv (Cornell University)Open access

Congruence modulo 4 for Andrews' integer partition with even parts below odd parts

Dandan Chen, Rong Chen

Abstract

We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of $\overline{\mathcal{EO}}(n)$ and further prove that $\overline{\mathcal{EO}}(n)\equiv0\pmod4$ for almost all $n$. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.

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Key concepts: Congruence relation, Modulo, Mathematics, Partition (number theory), Congruence (geometry), Combinatorics, Primitive root modulo n, Ternary operation