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Three proofs are given for a reciprocity theorem for a certain q-series found 7 in Ramanujan's lost notebook. The first proof uses Ramanujan's 1 ψ 1 summation the-8 orem, the second employs an identity of N. J. Fine, and the third is combinatorial. 9 Next, we show that the reciprocity theorem leads to a two variable generalization of 10 the quintuple(More)
In 2007 George E. Andrews and Peter Paule [1] introduced a new class of combinatorial objects called broken k-diamonds. Their generating functions connect to modular forms and give rise to a variety of partition congru-ences. In 2008 Song Heng Chan proved the first infinite family of congruences when k = 2. In this note we present two non-standard infinite(More)