Combinatorial proof of a congruence for partitions into two sizes of part
Abstract
Previous work showed that, for [Formula: see text] the number of partitions of n into exactly two part sizes, one has [Formula: see text]. The earlier proof required the technology of modular forms, and a combinatorial proof was desired. This paper provides the requested proof, in the process refining divisibility to finer subclasses. Some of these subclasses have counts closely related to the divisor function [Formula: see text], and we offer a conjecture on a potential rank statistic.
Fields of Study & Subjects
Advanced Mathematical Identities
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- International Journal of Number Theory
- Volume
- 22
- Issue
- 05
- Pages
- 1075–1084
- Publication date
- 16 January 2026
- Language
- EN