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arXiv · 2004.02185

A Family of Congruences for Rogers--Ramanujan Subpartitions

Nicolas Allen Smoot
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Abstract

In 2015 Choi, Kim, and Lovejoy studied a weighted partition function, $A_1(m)$, which counted subpartitions with a structure related to the Rogers--Ramanujan identities. They conjectured the existence of an infinite class of congruences for $A_1(m)$, modulo powers of 5. We give an explicit form of this conjecture, and prove it for all powers of 5.

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Nicolas Allen Smoot. 2020-04-05. A Family of Congruences for Rogers--Ramanujan Subpartitions. https://arxiv.org/abs/2004.02185

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