Work

Combinatorial proof of a congruence for partitions into two sizes of part

Year: 2026

Type: article

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.

Source: International Journal of Number Theory

DOI: 10.1142/s1793042126500569

Authors: Eli R. DeWitt, William J. Keith

Institution: Michigan Technological University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7124441553

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