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

2021/10/25 by Dandan Chen, Rong Chen, Chen, Dandan +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.12682

openalex publication_date 2021/10/25 · openalex created_date 2021/11/08 · openalex updated_date 2026/08/04

Abstract

We find and prove a class of congruences modulo 4 for Andrews' partition with certain ternary quadratic form. We also discuss distribution of EO(n) and further prove that EO(n)≡0\pmod4 for almost all n. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.

Related

• Multiplicative congruences for Andrews's even parts below odd parts function and related infinite products
• Distribution of the partition function modulo m
• Andrews-Beck type congrences modulo powers of 5
• Separable integer partition classes and partitions with congruence conditions
• Congruences and density results for partitions into distinct even parts