Abstract
In 2007, Andrews and Paule introduced the notion of broken k-diamond partitions. Let \(\Delta _k(n)\) denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, Wang and Yao, and Xia proved several infinite families of congruences modulo 7 for \(\Delta _3(n)\) by using theta function identities. In this paper, we give a new proof of one result of Wang and Yao, and find three new infinite families of congruences modulo 7 for \(\Delta _3(n)\).
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