Abstract
In 2007, Andrews and Paule introduced a new class of combinatorial objects called broken k-diamonds. Let Δk(n) be the number of broken k-diamonds partitions of n. By using MacMahon’s partition analysis, they found that the generating function of Δk(n) is an infinite product, which attracted many mathematicians to study its congruence properties. Recently, Radu and Sellers found infinitely many Ramanujan-like congruences modulo 3 for Δ2(n). In fact, they obtained 3-dissections of the generating function for Δ2(n) modulo 3 by using the theory of modular forms. In this brief note, we aim to present elementary proofs of Radu and Sellers’ results by using several theta function identities due to Ramanujan.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
