Elementary proof of congruences modulo 25 for broken kk-diamond partitions

Let $\Delta_{k}(n)$ denote the number of $k$-broken diamond partitions of $n$. Quite recently, the second author proved an infinite family of congruences modulo 25 for $\Delta_{k}(n)$ with the help of modular forms. In this paper, we aim to provide an elementary proof of this result.Comment: 9 page

Multiranks for partitions into Multi-Colors

We generalize Hammond-Lewis birank to multiranks for partitions into colors and give combinatorial interpretations for multipartitions such as b(n) defined by H. Zhao and Z. Zhong and Qp1,p2 (n) defined by Toh congruences modulo 3, 5, 7. Keywords: Partition congruences; multirank; Jacobi’s triple product identity; Quintuple product identity